{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The `extent` parameter in `geomImshow()` \n",
    "\n",
    "A list of four numbers: `[left, right, bottom, top]` that\n",
    "defines the image bounding box\n",
    "in terms of 'data coordinates'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "   <div id=\"BkZhOU\"></div>\n",
       "   <script type=\"text/javascript\" data-lets-plot-script=\"library\">\n",
       "       if(!window.letsPlotCallQueue) {\n",
       "           window.letsPlotCallQueue = [];\n",
       "       }; \n",
       "       window.letsPlotCall = function(f) {\n",
       "           window.letsPlotCallQueue.push(f);\n",
       "       };\n",
       "       (function() {\n",
       "           var script = document.createElement(\"script\");\n",
       "           script.type = \"text/javascript\";\n",
       "           script.src = \"https://cdn.jsdelivr.net/gh/JetBrains/lets-plot@v3.0.0/js-package/distr/lets-plot.min.js\";\n",
       "           script.onload = function() {\n",
       "               window.letsPlotCall = function(f) {f();};\n",
       "               window.letsPlotCallQueue.forEach(function(f) {f();});\n",
       "               window.letsPlotCallQueue = [];\n",
       "               \n",
       "               \n",
       "           };\n",
       "           script.onerror = function(event) {\n",
       "               window.letsPlotCall = function(f) {};\n",
       "               window.letsPlotCallQueue = [];\n",
       "               var div = document.createElement(\"div\");\n",
       "               div.style.color = 'darkred';\n",
       "               div.textContent = 'Error loading Lets-Plot JS';\n",
       "               document.getElementById(\"BkZhOU\").appendChild(div);\n",
       "           };\n",
       "           var e = document.getElementById(\"BkZhOU\");\n",
       "           e.appendChild(script);\n",
       "       })();\n",
       "   </script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%useLatestDescriptors\n",
    "%use lets-plot\n",
    "@file:DependsOn(\"org.apache.commons:commons-math3:3.6.1\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The default `extent` is derived from the image's array dimentions: `[-0.5, ncol-0.5, -0.5, nrow-0.5]`.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "   <div id=\"IWVmkR\"></div>\n",
       "   <script type=\"text/javascript\" data-lets-plot-script=\"plot\">\n",
       "       (function() {\n",
       "           var plotSpec={\n",
       "\"mapping\":{\n",
       "},\n",
       "\"kind\":\"plot\",\n",
       "\"scales\":[],\n",
       "\"layers\":[{\n",
       "\"ymin\":-0.5,\n",
       "\"mapping\":{\n",
       "},\n",
       "\"stat\":\"identity\",\n",
       "\"xmin\":-0.5,\n",
       "\"ymax\":1.5,\n",
       "\"xmax\":1.5,\n",
       "\"show_legend\":false,\n",
       "\"href\":\"\",\n",
       "\"geom\":\"image\",\n",
       "\"data\":{\n",
       "}\n",
       "}]\n",
       "};\n",
       "           var plotContainer = document.getElementById(\"IWVmkR\");\n",
       "           window.letsPlotCall(function() {{\n",
       "               LetsPlot.buildPlotFromProcessedSpecs(plotSpec, -1, -1, plotContainer);\n",
       "           }});\n",
       "       })();    \n",
       "   </script>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "// An 2x2 pix image by default has extent [-0.5, 1.5, -0.5, 1.5]\n",
    "val arr = RasterData.create(\n",
    "    listOf(\n",
    "        listOf(\n",
    "            listOf(150, 0, 0), listOf(0, 150, 0)\n",
    "        ),\n",
    "        listOf(\n",
    "            listOf(0, 0, 150), listOf(150, 150, 0)\n",
    "        )\n",
    "    )\n",
    ")\n",
    "\n",
    "letsPlot() + geomImshow(arr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## When does image `extent` need to be set explicitly\n",
    "\n",
    "Let's assume that our image doesn't exist in vacuum but is related to some data, \n",
    "and the image' bounding box in the 'data coordinates' is: \n",
    "\n",
    "- `(x, y) = (0, -1)`\n",
    "- `(width, height) = (8, 3)`.\n",
    "\n",
    "The image `extent` in this case would be: `[0, 8, -1, 3]`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import org.apache.commons.math3.distribution.MultivariateNormalDistribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "val cov0 : Array<DoubleArray> = arrayOf(doubleArrayOf(1.0, -.8),\n",
    "                                        doubleArrayOf(-.8, 1.0))\n",
    "\n",
    "val cov1 : Array<DoubleArray> = arrayOf(doubleArrayOf(10.0, .1),\n",
    "                                        doubleArrayOf(.1, 0.1))\n",
    "\n",
    "val n = 400\n",
    "\n",
    "val means0 : DoubleArray = doubleArrayOf(4.0, 0.0)\n",
    "val means1 : DoubleArray = doubleArrayOf(4.0, 1.0)\n",
    "\n",
    "val xy0 = MultivariateNormalDistribution(means0, cov0).sample(n)\n",
    "val xy1 = MultivariateNormalDistribution(means1, cov1).sample(n)\n",
    "\n",
    "val data = mapOf(\n",
    "    \"x\" to (xy0.map { it[0] } + xy1.map { it[0] }).toList(),\n",
    "    \"y\" to (xy0.map { it[1] } + xy1.map { it[1] }).toList()\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "   <div id=\"zxAKd1\"></div>\n",
       "   <script type=\"text/javascript\" data-lets-plot-script=\"plot\">\n",
       "       (function() {\n",
       "           var plotSpec={\n",
       "\"mapping\":{\n",
       "\"x\":\"x\",\n",
       "\"y\":\"y\"\n",
       "},\n",
       "\"data\":{\n",
       "},\n",
       "\"ggsize\":{\n",
       "\"width\":620.0,\n",
       "\"height\":300.0\n",
       "},\n",
       "\"kind\":\"plot\",\n",
       "\"scales\":[],\n",
       "\"layers\":[{\n",
       "\"mapping\":{\n",
       "},\n",
       "\"stat\":\"density2d\",\n",
       "\"position\":\"identity\",\n",
       "\"geom\":\"density2d\",\n",
       "\"data\":{\n",
       "\"..group..\":[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,2.0,2.0,2.0,2.0,2.0,2.0,2.0,2.0,2.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,4.0,4.0,4.0,4.0,4.0,4.0,4.0,4.0,4.0,4.0,4.0,4.0,4.0,4.0,4.0,4.0,4.0,4.0,4.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0],\n",
       "\"x\":[-3.1525867233091436,-3.1525213875261975,-3.15247928075785,-3.1168416835739547,-3.1069434591422684,-3.1004860464757678,-3.090025457441535,-3.077020239651052,-3.0665400573700916,-3.065474834856156,-3.0509841474854875,-3.0428202245347835,-3.033432618962566,-3.0255859118325557,-3.02104995069606,-3.0058260946626953,-3.00358563268912,-3.0024706393967264,-2.991732632111149,-2.991702390577509,-2.992586124039067,-2.999917121248113,-3.0005427141943013,-3.009213560858015,-3.034766756576451,-3.0473835020743327,-3.0893755990032776,-3.1527416931875845,-3.1584210629972036,-3.201313952420966,-3.3066767282092204,-3.3181586184338556,-3.325066766481088,-3.3332595012560837,-3.4144245225039143,-3.4835755436801277,-3.4975217427583267,-3.5058320026976886,-3.524775737272678,-3.5522162085681925,-3.586107275428109,-3.6011598784251517,-3.633189949038149,-3.638392241048058,-3.639772380694286,-3.648992468926399,-3.6594727796091764,-3.66077847655429,-3.661100260840669,-3.6607741056881284,-3.6607741056881284,-3.6596986754469785,-3.648992468926399,-3.6434466888989046,-3.6427244140831383,-3.6404046057250237,-3.6129076288236384,-3.604690059495383,-3.5797906472543044,-3.5732762541400485,-3.549214208955692,-3.5280981468113004,-3.4835755436801277,-3.469104806496339,-3.452418000782842,-3.3762413013462567,-3.3181586184338556,-3.254833490135754,-3.1537299511236214,-3.1527416931875845,-3.1525867233091436,2.639978823761443,2.6433351119727577,2.671367124488312,2.715956928899713,2.784059691573537,2.791216159994555,2.8022676156781925,2.8472137113963676,2.869087939905369,2.896488767950178,2.910894870294155,2.9371086939290976,2.94647040952262,2.9676845409244645,2.9982410265523542,3.0124798858017927,3.055989395448277,3.070482116216647,3.106645827687939,3.117811808939112,3.1331014661707357,3.189279474215943,3.2325042088572014,3.2639382902444414,3.298518391417007,3.3419004114955966,3.3799869160078817,3.421903257006825,3.463935316663278,3.5043871312290023,3.5445085282508018,3.5908810459058405,3.629352241909551,3.685093926330344,3.764180285560405,3.7842738352539076,3.794769167155822,3.8187943114070766,3.9078767840758655,3.9601860924020933,4.041235604176565,4.04412107280649,4.1256030176483645,4.193306127774596,4.225211517441579,4.291019942894637,4.349240050396025,4.401166146206322,4.456436868140909,4.5038974872674835,4.582796530537822,4.62185379338718,4.652488490325801,4.779345172029441,4.787270718633451,4.792837557842747,4.81487952167317,4.930829226006679,4.952687643879724,4.990892940808626,5.062957881026513,5.118104569125995,5.190075238312696,5.223217805246469,5.283521494372266,5.316175665912221,5.40615819539164,5.43940210640381,5.448938419618537,5.467728777171988,5.568327281286145,5.61435534486481,5.696347454007789,5.69840625672018,5.779772270111081,5.830837622150037,5.913214009631661,5.945189195357353,5.9687095988572665,6.1077829205245475,6.110606120603624,6.113024462390269,6.142604304914032,6.267764224004775,6.276023045849895,6.286279991812117,6.424827023026912,6.441439971096168,6.462079495157292,6.577130607768845,6.606856896342439,6.648479283579386,6.718785994158884,6.77227382158871,6.849949973712187,6.86485518613217,6.937690746834981,6.976839821668046,7.086590122339752,7.099167651779432,7.103107672081254,7.109928573058678,7.236862681899593,7.268524597327525,7.303599930333199,7.407075802038774,7.433941522573797,7.452234746569081,7.49336934636842,7.560879370036059,7.599358447820068,7.654483613945498,7.715404846598675,7.74083233039015,7.764775373066341,7.82760623532179,7.897978339197779,7.915625214163812,7.930192298312612,7.986448159208594,8.019770100942798,8.095609223558883,8.132693058598178,8.248736387739255,8.261026148805154,8.272027299345913,8.400025870089697,8.426443074051427,8.496809474453045,8.513163086149502,8.591859999297698,8.615851367782982,8.641274185360652,8.697829626218532,8.75727692454397,8.776564227939339,8.7919391190743,8.847348969157228,8.888283441077984,8.914693879881744,8.91805916161613,8.92269384979024,8.995794543280573,9.061523965946504,9.074492314937526,9.088110775036512,9.167478075847962,9.192451026059784,9.253527700282785,9.264458256585927,9.283363314176889,9.368234803780329,9.418944625529056,9.467913845215438,9.535578402392343,9.561486308535349,9.584361550775327,9.643105231215946,9.697363036831753,9.718810447324524,9.749778476021598,9.788177275592838,9.816899631334765,9.854161830357725,9.915195401267871,9.917405032512335,9.919620445884986,9.96338303921461,9.996238558874857,10.069822417682335,10.074086408532553,10.080612326514142,10.110660958253153,10.18137023897631,10.246029251760413,10.298954450341885,10.384758722168863,10.411446177006685,10.421721791011523,10.435535988364801,10.464632845597825,10.4856127104139,10.526491629026925,10.506449870044495,10.503685737591512,10.494418401143696,10.448519862754964,10.411446177006685,10.3346181509522,10.325041416466483,10.246029251760413,10.20430816075102,10.13902627355718,10.0990665203433,10.080612326514142,10.029756629266716,10.000227418786029,9.965681122518715,9.915195401267871,9.90341001399464,9.898680265363112,9.87700855997134,9.84686418032325,9.81189232924026,9.786654661719279,9.749778476021598,9.716750063880399,9.69054625923619,9.636038815303964,9.584361550775327,9.539261707398678,9.43572823956831,9.423723813904887,9.418944625529056,9.412227429292356,9.275147015353536,9.253527700282785,9.2311577465417,9.101186868242424,9.088110775036512,9.07769217067079,9.005534169349065,8.931730249461086,8.92269384979024,8.909457875836416,8.787005108418214,8.75727692454397,8.713909097295762,8.642247528714087,8.591859999297698,8.532794283061813,8.484668161558927,8.426443074051427,8.3795559391647,8.285063783883412,8.261026148805154,8.249664051772573,8.230040024036699,8.147563343625595,8.095609223558883,8.051348514523514,7.99764006224461,7.960845227775925,7.930192298312612,7.871090755417457,7.801406794573367,7.781127621298461,7.764775373066341,7.690238458154578,7.680512071814853,7.599358447820068,7.577326735228834,7.50822175091268,7.452436857454256,7.433941522573797,7.409314108000558,7.294992539442655,7.268524597327525,7.247055628457172,7.1480420078419105,7.109790371480045,7.103107672081254,7.09394428221162,6.969069875987893,6.937690746834981,6.900729124253047,6.811270536216654,6.77227382158871,6.7409336214264055,6.611146362615765,6.606856896342439,6.604732919097527,6.5999048544556125,6.494265636057554,6.441439971096168,6.38903469806125,6.307710968387511,6.2892871127998475,6.276023045849895,6.195722182448542,6.174238665753398,6.110606120603624,6.104099995904271,6.095588668051503,6.0169454303668335,5.945189195357353,5.930755880558941,5.915610833000796,5.877697282324039,5.8664355916484325,5.8201740598276235,5.816333408845807,5.805500088380747,5.800059982555769,5.800507914121056,5.818368338112219,5.824866342102313,5.832981816876174,5.846047886090263,5.864901109620556,5.878157255527309,5.8858860218846125,5.904524377162858,5.911369081714451,5.936178811468849,5.9389091736162385,5.939929321509595,5.945189195357353,5.974895416998864,5.983435544386307,5.992610650477898,6.007831426697937,6.025056496198564,6.03912522111683,6.044627799566603,6.062113430029672,6.070162998526127,6.091168273720589,6.096159945273824,6.098553653128683,6.110606120603624,6.131645089362026,6.1378236864770574,6.144788655107611,6.165944403375297,6.18136973691594,6.196733698648959,6.198377213447435,6.2186478139446955,6.227492400519591,6.242726398223946,6.250721537665807,6.254374271408288,6.276023045849895,6.2790095735985805,6.279724543601949,6.280480824032276,6.3083269770181865,6.315318844414287,6.323079887041882,6.334509499087604,6.345674305051773,6.358663202728874,6.358682140867657,6.371985148042953,6.380664591227076,6.387972913439132,6.394626381644313,6.399698299699416,6.4110308116007,6.413549810524978,6.416118645742653,6.429077060261635,6.429666735225098,6.430749931504856,6.441439971096168,6.4472689723450305,6.448051892234796,6.4495028754865,6.4720087357360825,6.477435047639544,6.488833574399335,6.503429449797316,6.519576668241731,6.5392924613697225,6.551772502799075,6.570066306544682,6.578178478625183,6.606856896342439,6.614804345182259,6.617109006402584,6.618837954567043,6.642399390051299,6.649502691525667,6.650867240466383,6.654576484954166,6.656978586261147,6.651260771823875,6.639937906923127,6.6368156862480046,6.630102774993317,6.606856896342439,6.59337826312456,6.58960872425882,6.574079751829878,6.54569356497481,6.521403134094733,6.494180644805038,6.441439971096168,6.437598223763672,6.435380511323741,6.425462007636899,6.379628117282925,6.347297052207713,6.324625764852385,6.276023045849895,6.270781214870654,6.267056981308926,6.24901814832886,6.21439452011786,6.186604655019927,6.161902625853042,6.110606120603624,6.103008587169112,5.9853007490726515,5.945189195357353,5.916460391420557,5.833012762692993,5.779772270111081,5.7228710385663515,5.678190111111865,5.61435534486481,5.550623302083876,5.51347442407549,5.448938419618537,5.39269645235677,5.337645297477561,5.283521494372266,5.223124420777305,5.179469617188007,5.118104569125995,5.046551569969177,5.007050840780293,4.952687643879724,4.931709502401549,4.90736893019705,4.849635821897179,4.787270718633451,4.7732899708950125,4.764283510917963,4.738200384234338,4.712274454949098,4.665253114071129,4.64917658442047,4.62185379338718,4.587521508478762,4.566959887060543,4.526201348298416,4.489824124482775,4.467684237831209,4.463328568921259,4.456436868140909,4.399130384346524,4.3627681678467525,4.339091674060407,4.291019942894637,4.284410539393498,4.281084251375086,4.276785684979306,4.235044054848862,4.210502474589838,4.193671671973329,4.184053793174973,4.163269062053136,4.1570561675280615,4.131823154038257,4.1301234004990715,4.129448013566526,4.1256030176483645,4.098489823523719,4.09195938586922,4.078456559059685,4.062317780052913,4.04374285581663,4.017770077287036,3.976483927772179,3.96914550379155,3.965449308862331,3.9601860924020933,3.8870681301074956,3.8198546733543353,3.8064368310879058,3.794769167155822,3.7176342198002086,3.6370236015277104,3.629352241909551,3.6286677159755083,3.6279100556116095,3.5424365196973984,3.463935316663278,3.456716495593934,3.449859082903467,3.3820353055794268,3.3812833998589564,3.3094375745841926,3.304842398872374,3.298518391417007,3.237606355647774,3.1961403826910626,3.174809127800236,3.1331014661707357,3.118398482274788,3.110525423932706,3.0978063734328227,3.0672062896930887,3.0358112577409937,3.0192110898623215,2.989570171664888,2.980157112275128,2.9773265913713765,2.9676845409244645,2.9351046110078363,2.923356350975782,2.9103247895078974,2.8976276059907455,2.8742191805348565,2.861570468439674,2.84887916960428,2.83444549539775,2.8290924592564766,2.8022676156781925,2.801343376033407,2.801080105636948,2.800818270356003,2.7666707322492394,2.7572017025831252,2.7474222206830845,2.736187339995201,2.7195008244018206,2.706365480292291,2.7002177280574307,2.683977529650252,2.6753288819368306,2.6496810184733697,2.645936752448378,2.643875824321471,2.6368506904319213,2.598209530641972,2.582624159563651,2.5509712443176786,2.546779042758561,2.5094143386848202,2.497106050233329,2.4714337651856493,2.43912066763715,2.4197435467624073,2.3806003685197545,2.362652704999797,2.32707967821797,2.3198038616102457,2.306016839939378,2.254245702457667,2.2178952337161286,2.1877787551049694,2.140599914693106,2.1174611532569214,2.0921962147075144,2.0275954722972536,1.975182989446835,1.9224977383000583,1.8318249223681393,1.8097660642005629,1.7962511898616231,1.6933121415802583,1.6491502098964768,1.6443491389542917,1.638020891105727,1.4975483182851548,1.4789322137080196,1.455176459705065,1.3449519520077606,1.3135152884617485,1.2764821877002657,1.187399202434273,1.1480983632154764,1.1044163370941638,1.0290213762389566,0.9826814379692053,0.9247542413767276,0.8816261849056186,0.8172645127229332,0.7479325182294323,0.7086444625286026,0.651847587476662,0.6238463663889595,0.5561149564450991,0.5045717301377808,0.4864306622303909,0.44754044830308537,0.3825872541170927,0.32101373698411884,0.2590701056824267,0.19715215732391744,0.15559681173784767,0.13137520917352852,0.027183750948026386,-0.003197724122965262,-0.009820113508424377,-0.019005220969291692,-0.15745081706970865,-0.17523703875469554,-0.19240904341080967,-0.33806454987814405,-0.3406539640009676,-0.3427101753486612,-0.3547398347722339,-0.477479947083399,-0.5060708892472388,-0.5477935165355117,-0.6215788309191437,-0.6714878144935108,-0.7166045736869777,-0.8141125647348879,-0.836904739739782,-0.8480617702170941,-0.8643994426783057,-0.9545472628276621,-1.0023216649860536,-1.0496027263942502,-1.0992329223518733,-1.136869316679662,-1.1677385902323252,-1.218339523341056,-1.2620125514330174,-1.294841569631568,-1.3331555154785968,-1.3678152789575404,-1.392985003050124,-1.4333920199830454,-1.4905707500891365,-1.4961635499602766,-1.4970263805871453,-1.4985724407248684,-1.5580907555249301,-1.5929632837213226,-1.614813135778149,-1.66398936597114,-1.665959579393184,-1.6670401481519384,-1.669262049270022,-1.7195354404282592,-1.7462327487606175,-1.7680605192477028,-1.7916598861729063,-1.80617374651231,-1.8110589961548413,-1.8294062912174116,-1.8508171972259366,-1.8588948229884186,-1.86781710484884,-1.8835776839767266,-1.8952997381765178,-1.9008706794907244,-1.9013088535856544,-1.9027376915210108,-1.8916442754156013,-1.8827640543671897,-1.877109262072286,-1.8645309035315796,-1.8294062912174116,-1.8219042642504828,-1.819626265345955,-1.811238561831912,-1.7733250288130362,-1.7500028066972373,-1.7205987622151144,-1.6641820604225783,-1.6640899878895943,-1.6640542982465258,-1.66398936597114,-1.6090406736701794,-1.5816629318803197,-1.5496851110310104,-1.4985724407248684,-1.4856731084422332,-1.4772299955834347,-1.4094785326918382,-1.3331555154785968,-1.3315063405700225,-1.3296507668113748,-1.2347531987179954,-1.1677385902323252,-1.1320404920235578,-1.049182355282912,-1.0158947484837726,-1.0023216649860536,-0.9792125430480905,-0.8865125228119082,-0.836904739739782,-0.7667211545351043,-0.7449867408826285,-0.6714878144935108,-0.5946106244228675,-0.582336696013618,-0.5060708892472388,-0.43937749927331016,-0.4047042566757302,-0.3406539640009676,-0.28806874422429374,-0.21783954725814603,-0.17523703875469554,-0.14367832725708585,-0.020987106018295343,-0.009820113508424377,-0.001498611879276801,0.07428258548756883,0.14586651386972527,0.15559681173784767,0.16694710236276222,0.30283203729863395,0.32101373698411884,0.3406727861731387,0.45796875083176314,0.4864306622303909,0.5228151973606394,0.598200189159555,0.651847587476662,0.7254169532175538,0.7536351132811516,0.8172645127229332,0.8418054433196689,0.8889178080378013,0.9446981327318449,0.9826814379692053,1.0361871407657715,1.0957513946738073,1.1184979202911176,1.1480983632154764,1.1838220484453847,1.2045482893268398,1.233551899874711,1.2366766017997035,1.2653832033770671,1.2746072432615918,1.3018284213318951,1.304594554896605,1.305888846327333,1.3135152884617485,1.3271759278111617,1.3290572589658032,1.3319690179002581,1.346541919451373,1.3507661458245748,1.3616807267916844,1.371284503073194,1.3806116957238572,1.4052637001029868,1.414356671687493,1.4296028627318895,1.445288967367036,1.4789322137080196,1.4999851235547155,1.5114785344219515,1.5714184679436558,1.6443491389542917,1.6463755170400205,1.6487586979678444,1.7410340235086768,1.8097660642005629,1.8395451706396369,1.8959924536068087,1.9460940061874226,1.975182989446835,2.0546402819287053,2.0677282854504284,2.140599914693106,2.1660419020625588,2.2303941112992662,2.2804454380147146,2.306016839939378,2.3562373228091182,2.412586243489793,2.4714337651856493,2.5206005252585495,2.6288243049151134,2.6368506904319213,2.639978823761443,9.111905259213012,9.11602538181225,9.10433880384159,9.088110775036512,9.061836466525456,9.006556368933728,9.020036976951,9.088110775036512,9.111905259213012,2.982402662530986,3.0312795617075095,3.1159018701167547,3.1331014661707357,3.1676522757071632,3.2367507867465317,3.298518391417007,3.3498076587551093,3.443654084675586,3.457835261155738,3.463935316663278,3.480475086215815,3.5722882539311804,3.629352241909551,3.69033830105724,3.758614691456817,3.794769167155822,3.8147214788738424,3.914583946465074,3.953835354626955,3.9601860924020933,3.9680102797758554,4.110036555306335,4.1256030176483645,4.142163722993274,4.272896185328786,4.291019942894637,4.310018173267027,4.433864265320546,4.456436868140909,4.482573742883702,4.586687571375933,4.62185379338718,4.670169606905766,4.7292004397251866,4.787270718633451,4.862741777793309,4.883279550264827,4.952687643879724,4.9918509801141,5.1048051312236495,5.114880287463238,5.118104569125995,5.1248157607113995,5.239402249330579,5.283521494372266,5.362602423457611,5.37379350008738,5.448938419618537,5.487652383135167,5.604041442535674,5.611985403031614,5.61435534486481,5.61880572711379,5.741835257726505,5.779772270111081,5.849193017792157,5.870473626025966,5.945189195357353,5.999667838576178,6.08314647456459,6.110606120603624,6.125992337703623,6.169243451884769,6.247219152025584,6.276023045849895,6.355923337501647,6.359935581324141,6.441439971096168,6.476306298257494,6.550158649340851,6.587335743286507,6.606856896342439,6.658684141447784,6.7033988431384355,6.77227382158871,6.82875871236711,6.898158865445515,6.937690746834981,6.962901630620205,7.098839015083655,7.103107672081254,7.106127449079711,7.130865795620595,7.25524708126677,7.268524597327525,7.284913821335392,7.407554735818737,7.433941522573797,7.4667790144569555,7.564252928663366,7.599358447820068,7.636606085972257,7.736711290077835,7.764775373066341,7.788646152679915,7.888280093152709,7.920339075980591,7.930192298312612,7.96037186118148,8.033548834118395,8.095609223558883,8.15319286984488,8.2276760759403,8.261026148805154,8.342743654232985,8.34875170387286,8.426443074051427,8.437679580237148,8.444533966679055,8.458582561196573,8.487647679991278,8.512329922787625,8.529067530640694,8.543543574697294,8.551543591675832,8.549462329687415,8.557994197338179,8.557994197338179,8.519340224433753,8.514906740762175,8.49350851387566,8.455237895355987,8.426443074051427,8.372559490102782,8.325019221738534,8.288461091881079,8.261026148805154,8.21174793721035,8.176097470197833,8.138258974257992,8.095609223558883,8.068295168272742,8.052549028882703,8.00131835907262,7.941668945100211,7.933641872040049,7.932058255307016,7.930192298312612,7.86036291509205,7.807085100397822,7.78689812764048,7.764775373066341,7.703118685181035,7.636881931247128,7.616621482551697,7.599358447820068,7.531332868280966,7.51275268815154,7.433941522573797,7.40080634149208,7.27153542466962,7.268524597327525,7.2664861845040765,7.2269790792160595,7.1095709879649736,7.103107672081254,7.09623008256607,6.950580455623765,6.937690746834981,6.921839366057066,6.808477262858245,6.77227382158871,6.706753110129554,6.6817371225964095,6.606856896342439,6.56591020592562,6.488195630110887,6.457510729156109,6.441439971096168,6.367923061488268,6.3569676578679335,6.276023045849895,6.259660575250344,6.2394237259451195,6.168269810345981,6.110606120603624,6.0767795245193135,6.034705020923077,5.9845375796786975,5.945189195357353,5.8854058064633605,5.784508250816538,5.781588323797941,5.779772270111081,5.774138707879844,5.666958008505601,5.61435534486481,5.555385847934936,5.456020982571914,5.448938419618537,5.446802405477586,5.44464732311183,5.442585542716774,5.390838990406179,5.3610617755878085,5.3610617755878085,5.361362077481795,5.348805483283014,5.351745073455019,5.356501605699737,5.370838073135943,5.384278851909082,5.393751594575294,5.410654213172705,5.419499096094258,5.448938419618537,5.4584907658050685,5.461699252777651,5.466848065216835,5.502195457767961,5.522168854160871,5.543290494768888,5.553138968733638,5.57603562101743,5.584376189857462,5.61435534486481,5.621063123875775,5.6232084081489315,5.625577664690288,5.65709603449859,5.669182795670029,5.681893122479595,5.687808378031107,5.705596449188789,5.716333839514853,5.724186050947797,5.7355134164278425,5.74147348448885,5.757843007924134,5.7615986002643975,5.763932262910888,5.779772270111081,5.786677631730015,5.788033999870274,5.7897692623342945,5.812821581316067,5.819047448707325,5.8271360213142085,5.83805621845214,5.848705046480024,5.862159662412623,5.862254945792884,5.87662657196419,5.8854272487258275,5.893352674075846,5.901455217356592,5.90615634163661,5.918117548881364,5.921491045621204,5.923331110829649,5.934517898280319,5.935374091384238,5.935775965096893,5.942313366428895,5.942397312177286,5.942342110387328,5.942512817870956,5.942512817870956,5.942334680833895,5.936685985592421,5.936374209078991,5.935461738887531,5.926746961754935,5.9255759366667515,5.923138242430598,5.9150705912958905,5.9129249662454395,5.909081358231706,5.904561758169498,5.902491208447991,5.899046946135648,5.899204488907358,5.899204488907358,5.901255861255519,5.907439606199723,5.907439606199723,5.911896556960217,5.927172342864116,5.927691550511986,5.92986231890492,5.945189195357353,5.951730090772534,5.952940965455722,5.953706709420423,5.9618976629953,5.962873890697811,5.960268092867791,5.945189195357353,5.935767962234451,5.934113855459675,5.92091450141703,5.882444283008603,5.851654831096457,5.8184083888169145,5.779772270111081,5.733280636485313,5.672204234308165,5.635737060538132,5.61435534486481,5.572348783467099,5.505577238544625,5.448938419618537,5.391474444766958,5.328234148031608,5.283521494372266,5.259984158441421,5.220476184367291,5.158038883385025,5.118104569125995,5.067609973351866,5.01604496251648,4.984011853418972,4.952687643879724,4.904997511016672,4.86421780604476,4.829104814625422,4.787270718633451,4.756346771049852,4.734012494173131,4.692361454042873,4.657140691312234,4.634638314744786,4.630608403256117,4.62185379338718,4.58240132797471,4.566549643529106,4.550336707702506,4.545168402665583,4.522145098532606,4.512241573112906,4.50063219616956,4.490230974343053,4.4846879920381575,4.458102279270626,4.457720347131895,4.457429451539923,4.456436868140909,4.413400762708605,4.397705129473698,4.357945270485841,4.311744320859761,4.299495221415674,4.295583377369763,4.291019942894637,4.211707447835822,4.129174209009907,4.127232544843878,4.1256030176483645,4.107175865967612,4.036149564319114,3.9601860924020933,3.945155764275439,3.927626109853165,3.859104270090018,3.794769167155822,3.7745424976601356,3.7545376724069346,3.696617108248299,3.629352241909551,3.620436511286359,3.6132878804234885,3.5776931921098267,3.551484405580535,3.4946212326772716,3.4826324999392337,3.463935316663278,3.420639094296206,3.3953972447661656,3.363970253272175,3.33209221583701,3.313579518496878,3.3089356851195406,3.298518391417007,3.2591400360120097,3.242331251854771,3.217409960753808,3.2165087128207315,3.1843569208758513,3.1734664547857436,3.1421756905378517,3.139015860501358,3.1379075031887282,3.1331014661707357,3.1037339514445863,3.095922145850259,3.0876722313057456,3.073516099957116,3.059551434156594,3.0456375464917347,3.043571094065853,3.026797196982174,3.0168281222230506,2.9997450321849684,2.9920374130365612,2.9869709847491857,2.9676845409244645,2.949639919575487,2.9436838016275377,2.9294270312908175,2.9028169582328704,2.875106566138548,2.8517176976546255,2.8022676156781925,2.7982043959181864,2.795959220069169,2.7885189358043583,2.736373771383903,2.696314670978282,2.6750490501463835,2.6368506904319213,2.6146324662681346,2.6010656574828817,2.5648224905803954,2.5570103152056527,2.5109731958887886,2.4983872384063144,2.4714337651856493,2.4423522043860526,2.4259808732445096,2.3860925274527647,2.3808661532030344,2.340246341653229,2.3284897484324167,2.306016839939378,2.261439164154786,2.2255755308577534,2.1854129488646885,2.140599914693106,2.0968289141405974,2.0254224876245486,1.993376367429673,1.975182989446835,1.9265553898722834,1.8757120357395545,1.8097660642005629,1.7542630977146283,1.665434233637499,1.6443491389542917,1.6337810612639991,1.607582155219725,1.518152894168753,1.4789322137080196,1.401326477369313,1.3841895582726655,1.3135152884617485,1.2776438939573573,1.15225698014648,1.1480983632154764,1.1453580748963939,1.1286133025912326,1.0021413917051145,0.9826814379692053,0.9538919636757353,0.8621778175434835,0.8172645127229332,0.7364802351655939,0.7334620411311823,0.651847587476662,0.6103847098460822,0.5239549327929272,0.5007138761253564,0.4864306622303909,0.406096978653542,0.38526056066956205,0.32101373698411884,0.3102049050536957,0.2913575015988936,0.2094471528807027,0.15559681173784767,0.07943307094521579,0.06837658211196374,-0.009820113508424377,-0.06448090038199972,-0.1624754902520955,-0.17523703875469554,-0.1787840292724816,-0.18500503725934347,-0.2919310455552191,-0.3406539640009676,-0.41248064199049317,-0.4442783716532741,-0.5060708892472388,-0.5389334384713091,-0.6543268071996957,-0.6714878144935108,-0.6885180795383534,-0.8032763671583947,-0.836904739739782,-0.917821679553267,-0.9261269188648291,-1.0023216649860536,-1.0208979649062395,-1.0400858777936128,-1.0965689337510538,-1.1677385902323252,-1.1694800970015389,-1.1705514986322516,-1.1724256852530428,-1.219698170750636,-1.2422802510816457,-1.259227898393012,-1.26445130141887,-1.2800443913899828,-1.2831946758360742,-1.287602413658853,-1.2881752280452328,-1.2794645993125884,-1.2745103216867166,-1.2690366949179959,-1.2468568138124976,-1.2440597153494135,-1.2271665923923187,-1.211972790653836,-1.171713680005499,-1.1705141639062684,-1.1697492633565418,-1.1677385902323252,-1.1235192004476309,-1.1063521297507162,-1.0728835813285822,-1.0509644461760854,-1.029358740837842,-1.0191626968783183,-1.0023216649860536,-0.9481576844381854,-0.9041044121248052,-0.8683720228314824,-0.836904739739782,-0.7614857566237063,-0.7368323875908653,-0.6714878144935108,-0.6388549224730999,-0.5294324304261506,-0.5060708892472388,-0.48364864874912517,-0.3678152323665609,-0.3406539640009676,-0.3100720183776966,-0.2067870182842073,-0.17523703875469554,-0.14468731825650316,-0.03358702864470331,-0.009820113508424377,0.01157832623347943,0.14945970175683154,0.15559681173784767,0.16020996500992268,0.18003662406279908,0.29890191241483954,0.32101373698411884,0.35820279274358136,0.42454830659161846,0.4864306622303909,0.5407054334663242,0.6507511105202308,0.651847587476662,0.6521632343675083,0.6527316973625883,0.7625445382565372,0.8172645127229332,0.8758109347741847,0.9598558572317817,0.9826814379692053,0.9921460525269605,1.0213879203760827,1.1139974778584332,1.1480983632154764,1.219034907546856,1.2377169822798422,1.3135152884617485,1.3655305632273533,1.4590651062429227,1.4789322137080196,1.4896962545447865,1.513681261009192,1.5929687979159075,1.6443491389542917,1.6873123590811776,1.7361730194192075,1.7698043907606298,1.8097660642005629,1.8474862471883515,1.8828342441907857,1.9235501275391416,1.975182989446835,2.0031737649292225,2.041738001164709,2.0950254319296624,2.140599914693106,2.2113607721356745,2.239236204016355,2.306016839939378,2.340030500987016,2.44673800558016,2.4714337651856493,2.4849173241682667,2.5796991707831145,2.627554492163136,2.6368506904319213,2.64630936256917,2.7742232612791327,2.8022676156781925,2.8300885003619207,2.9442628164192675,2.9676845409244645,2.982402662530986,-0.48751309743039606,-0.48274829441175005,-0.4888528954592788,-0.5060708892472388,-0.5611042038047929,-0.6290079139181142,-0.6616336638823523,-0.6714878144935108,-0.6783475938036836,-0.6862288697744976,-0.6862751222511347,-0.7044453043320722,-0.7095343904500528,-0.6974159021251753,-0.6714878144935108,-0.593049407282658,-0.5806517698780578,-0.5060708892472388,-0.48751309743039606,3.4948089942217475,3.566502893477473,3.6119368189122447,3.629352241909551,3.665386527041303,3.737583570154559,3.794769167155822,3.871884604446583,3.8856308329632014,3.9601860924020933,4.019214117385756,4.069835041691183,4.1256030176483645,4.177883756299348,4.239586154426677,4.291019942894637,4.340052610601267,4.410276474758993,4.456436868140909,4.496202213855083,4.594378958440812,4.62185379338718,4.641916171721485,4.728676358426236,4.776288821735818,4.787270718633451,4.807991491938392,4.90209132957003,4.952687643879724,5.024292781383545,5.060063077075668,5.118104569125995,5.145581272817665,5.220579906456715,5.26681894724411,5.283521494372266,5.31756385318266,5.390830133884661,5.448938419618537,5.51598933560431,5.5617543577823625,5.61435534486481,5.642161732857275,5.730774500510185,5.768040610410766,5.779772270111081,5.804391393040143,5.89096040634492,5.945189195357353,6.008217457245992,6.082456644408705,6.110606120603624,6.121007969991203,6.1387616275240475,6.220075056109563,6.276023045849895,6.315086080718897,6.36290456067721,6.401573410942017,6.441439971096168,6.486184628433664,6.536609451973533,6.569768701668558,6.606856896342439,6.662286666249273,6.760084949978372,6.767223675853863,6.77227382158871,6.78089658971977,6.919849362911272,6.937690746834981,6.9538901329999945,7.057106453673352,7.098315924979749,7.103107672081254,7.108456593044902,7.259493145018137,7.268524597327525,7.276152680843534,7.314687559876633,7.408135197190438,7.433941522573797,7.507328536507256,7.598461039547772,7.598724770229968,7.599358447820068,7.633055483324364,7.641819440134693,7.63681383474438,7.622852628909522,7.617905369334828,7.612091593527037,7.599358447820068,7.553343468689507,7.526466729832567,7.480857142813228,7.433941522573797,7.387777771517612,7.299271771515452,7.2773498954558615,7.268524597327525,7.254823671722946,7.127387550804459,7.103107672081254,7.078249562959263,6.95496698865446,6.937690746834981,6.917705153966882,6.799835537350258,6.77227382158871,6.718486445424434,6.678264683971827,6.606856896342439,6.571545248448457,6.526062485558231,6.474640897289261,6.441439971096168,6.378278790752102,6.294501389862919,6.283636639744177,6.276023045849895,6.217201813398246,6.19014864573775,6.110606120603624,6.096639152865134,6.07887600595723,6.005397565547348,5.945189195357353,5.9118515376801195,5.862535018056198,5.812145426420775,5.779772270111081,5.702306206904506,5.6941374481808325,5.61435534486481,5.550497683658472,5.511826919329621,5.448938419618537,5.382457539094084,5.3487211858289285,5.283521494372266,5.239757333555982,5.150405602353876,5.132643946591463,5.118104569125995,5.081505670976574,5.0684218756988155,5.0684218756988155,5.057307273700278,5.045782825832788,5.045782825832788,5.044132653746249,5.044857959003533,5.047080265201112,5.047835062420564,5.058493452792604,5.065489635768687,5.074720043676853,5.0836829191773845,5.089733231777684,5.118104569125995,5.118915516216061,5.119121363389574,5.119494128511073,5.158952822059746,5.172037984440001,5.199137188977035,5.200035957986914,5.230056299981655,5.244648396981697,5.283521494372266,5.2900848003949275,5.292707726799685,5.297721349006633,5.336988556832795,5.358466838964912,5.381151237006806,5.396160521169703,5.4162078399113245,5.423682600123341,5.448938419618537,5.46170539719628,5.465580764089497,5.469929025186147,5.494756443117032,5.506292421956843,5.51817608317193,5.5226286038173935,5.537218222560117,5.546826967454871,5.551863655705821,5.561125104345084,5.566899626362858,5.576667472024004,5.580757550058202,5.584117295226024,5.5972347310128185,5.598672282923436,5.60021647808302,5.61435534486481,5.616864566092799,5.61719060109912,5.617653939615783,5.6356908498121445,5.638424326606854,5.64199519512526,5.653677987490264,5.658344087918886,5.663490396369834,5.669267588680881,5.674436897883876,5.678816501073188,5.680715686234407,5.6843586698341735,5.686132690138731,5.686320474272696,5.686943969177971,5.684517049347853,5.683617955144193,5.682378758602294,5.677882057573489,5.674959659555263,5.6716623779825355,5.666397982249828,5.659495754469509,5.655823613633242,5.651134919852488,5.637713880497117,5.635469024724147,5.632757611150103,5.61435534486481,5.6112269906361565,5.610711656510166,5.609348548566571,5.585305360676159,5.579988266748314,5.563999127064264,5.553738346857935,5.542314112548285,5.517429024997719,5.501201141926231,5.491217129977558,5.478305296266946,5.448938419618537,5.40592518281848,5.335428481934063,5.298501950859187,5.283521494372266,5.268495767056706,5.23106690202491,5.146229606914295,5.118104569125995,5.050704127547046,4.975699892656149,4.9639564538931875,4.952687643879724,4.899063339388448,4.8670094801134525,4.843474278567097,4.805284528144471,4.79657278533216,4.794180075680208,4.787270718633451,4.756893662795218,4.748363641034809,4.733235464179373,4.7200279555231734,4.699907172692615,4.677320393026518,4.639892818458906,4.632806720250031,4.628690256518318,4.62185379338718,4.561955281925135,4.520870833483125,4.4895296882842874,4.456436868140909,4.40591674495176,4.351452456899407,4.318616064596425,4.291019942894637,4.22966295837845,4.158993532765775,4.141870973483403,4.1256030176483645,4.05977644693265,3.9959283879730716,3.9797296608428816,3.9601860924020933,3.904897110747486,3.8592757693017976,3.8316301111150253,3.794769167155822,3.760521217398068,3.73454863985922,3.6905605352741997,3.629352241909551,3.6217543021706273,3.6167085106646404,3.5989090206899537,3.5580565001846427,3.51231680240733,3.495419043130788,3.463935316663278,3.4394674363753452,3.427683652546854,3.4083941076386495,3.3921793745605004,3.361657067572539,3.347561129641867,3.320402708412206,3.31254909697077,3.309877356761712,3.298518391417007,3.2771697698350355,3.271770777948255,3.2657592411875944,3.2473445132114485,3.235779614090066,3.220236200533308,3.218571503182634,3.200055890763463,3.1866778740101154,3.167287589651597,3.1578513344132437,3.1516745251098115,3.1331014661707357,3.1075620552856513,3.0975973364825338,3.067867868316843,3.0563949380342637,3.018909050799998,3.000946311791016,2.9676845409244645,2.941368167549781,2.925716455004764,2.880449346644606,2.8679982209018906,2.8273486691626717,2.818308694315207,2.8022676156781925,2.7575695966509564,2.7313549344121,2.700418731775705,2.6641270623694115,2.649660447612246,2.645759413443341,2.6368506904319213,2.592690696488419,2.571494712008863,2.5415499173507827,2.522776633382496,2.4998317897138556,2.4911433819591373,2.4714337651856493,2.434425882877729,2.4130222109582293,2.3709306110826116,2.306016839939378,2.3058196881982482,2.3056211969935605,2.2194020790986455,2.140599914693106,2.1316178506189605,2.1172354197413217,2.031985664213048,1.975182989446835,1.9323340946252205,1.866567251109669,1.8351369344782213,1.8097660642005629,1.745030700920104,1.6686020006251043,1.6569193626335856,1.6443491389542917,1.5675869817949453,1.5033110042003592,1.4789322137080196,1.4755914425659737,1.467396787066778,1.3574643508384998,1.3135152884617485,1.2450928495717477,1.2201843446281329,1.1480983632154764,1.0801119490091953,1.0425154559798964,0.9826814379692053,0.951714643485138,0.8970594781595986,0.8514960378527485,0.8172645127229332,0.7738975728222313,0.743612945093238,0.716767689373178,0.6916837748993734,0.6718606387998713,0.667572120946458,0.651847587476662,0.632891117543954,0.6279738950225395,0.624023668430552,0.6093403144909537,0.6027762452751366,0.6004709246506588,0.5998927891363435,0.5994089896753145,0.6079228372015963,0.6265723822740377,0.6296266931855046,0.6367508838147895,0.651847587476662,0.6903689417299432,0.7089622964123015,0.7597317146773035,0.8172645127229332,0.8411410630204763,0.8714482185316035,0.9410864868824307,0.9826814379692053,1.0597397044662493,1.0755322467261657,1.1480983632154764,1.2020621770486848,1.2607197748799415,1.3135152884617485,1.37683086381454,1.4118798542249316,1.4789322137080196,1.5508675953121633,1.5731144943322954,1.6443491389542917,1.6943899593199951,1.806505013521031,1.8097660642005629,1.8107084922510248,1.811712148276242,1.896045908429783,1.975182989446835,1.9802730675996205,1.9840121874783518,2.027619016692382,2.054381439024427,2.117122372691844,2.128368524352033,2.140599914693106,2.2073127597967845,2.268138495435606,2.2881193936379063,2.306016839939378,2.381916174250053,2.4328071009447996,2.4714337651856493,2.476227213595531,2.4844477275709,2.581814712335433,2.6368506904319213,2.697251782149708,2.762139434495685,2.8022676156781925,2.823064143124607,2.965695893840908,2.9676845409244645,2.9693533978873674,3.1213007217614477,3.1331014661707357,3.1504937484776248,3.254641003841776,3.298518391417007,3.3765117099026227,3.3926392056784103,3.463935316663278,3.4948089942217475,3.3454196001911845,3.4615664069844208,3.463284003378247,3.463935316663278,3.4655606233883933,3.5810862418595253,3.629352241909551,3.700952430971313,3.735885665516655,3.794769167155822,3.8276717718227378,3.9558095818208656,3.9601860924020933,3.9634731172016444,3.998277796824823,4.11398967830273,4.1256030176483645,4.1393872718559575,4.272580355028497,4.291019942894637,4.31179525303301,4.428701868915093,4.456436868140909,4.492022053825538,4.573489669942877,4.62185379338718,4.701375373544977,4.706357459611402,4.787270718633451,4.832099007479332,4.949801515345992,4.95182593291846,4.952687643879724,4.954780485632337,5.067991294434032,5.118104569125995,5.187099070174694,5.230164564317338,5.283521494372266,5.308597661205797,5.385736640347368,5.432423563106861,5.448938419618537,5.482121776827627,5.556041215136778,5.61435534486481,5.678967194460498,5.734717369443949,5.779772270111081,5.800215945616204,5.848210610182933,5.912209229575703,5.945189195357353,6.012742695542634,6.108037211759033,6.109331673417973,6.110606120603624,6.1823606845189865,6.23885731830233,6.250918125255987,6.276023045849895,6.304285736313474,6.317644888609491,6.329881145592628,6.3381646893250405,6.348581167970757,6.338176076844617,6.329909810022251,6.326524925555933,6.309631235372963,6.276023045849895,6.25055904069818,6.2341371511607555,6.171514186913116,6.110606120603624,6.083209940122172,6.041215330015321,5.9818997012944735,5.945189195357353,5.873295337592408,5.832159174678315,5.779772270111081,5.757821211888164,5.687521012595884,5.632182299816861,5.61435534486481,5.589610210716463,5.488995651089944,5.448938419618537,5.402785050281405,5.334696150198543,5.283521494372266,5.226562516582435,5.179784293697786,5.118104569125995,5.045386122512269,5.01506918513285,4.952687643879724,4.927867017412169,4.896986790535543,4.853785418117727,4.793768862761775,4.7889849327320295,4.788676870186155,4.787270718633451,4.76995408099112,4.769122539897587,4.769383163001857,4.771299982729346,4.774028306442453,4.775215384821646,4.787270718633451,4.790594160707952,4.790740742144365,4.790770836237508,4.812210602581143,4.81611421838776,4.8183925800728264,4.834062285041934,4.8424414934446,4.8504647664197655,4.856843569384225,4.870435947441605,4.882636507204065,4.887975311755206,4.9016215961597,4.910644469965712,4.9328682394110235,4.937342847864658,4.940396875156191,4.952687643879724,4.976036163513623,4.98282393027533,4.997232563014906,5.015837639513515,5.036192275291764,5.058003510863326,5.083759463098762,5.095817648841345,5.10211525590036,5.118104569125995,5.149798058478122,5.162819872176515,5.191276226198939,5.196773357768507,5.22862643725092,5.243061985598853,5.283521494372266,5.286434931651943,5.287416748210976,5.288680548484862,5.322404735459884,5.3332085228093185,5.3448857549982325,5.352275992174066,5.366670848662599,5.376777353270898,5.380212952720031,5.38986069675259,5.395280493304657,5.401808441104542,5.405614282688422,5.408731964499712,5.415877400917401,5.417165644155142,5.419232327335351,5.4271586261129166,5.4275407725051945,5.4289471031799525,5.438438748493374,5.438532141439303,5.439165713900659,5.448938419618537,5.449690203817319,5.449742844818049,5.449818004272538,5.45758673609093,5.458017725070006,5.45850621789139,5.460379397620532,5.460527803428844,5.4602775355326685,5.455776631058841,5.455776631058841,5.4553310649198465,5.448938419618537,5.443106238284445,5.442552937094604,5.4407058255417,5.421543805734652,5.417499293235295,5.406080653320583,5.3925829947661015,5.381093215635978,5.356756189089934,5.3473257458959065,5.32964955385688,5.315690459120647,5.283521494372266,5.233576463705067,5.153315029475744,5.118104569125995,5.0627285686888435,5.02643662349727,4.996066313648704,4.952687643879724,4.935220063625069,4.9280596980492835,4.89036142949754,4.875881994735362,4.83357270141847,4.812001099489553,4.787270718633451,4.7363591895789146,4.694160489107263,4.6557254350163735,4.62185379338718,4.567054662763427,4.50302067643954,4.476824233468909,4.456436868140909,4.387117970217128,4.306824324534848,4.298659852136712,4.291019942894637,4.2188867899046,4.152599713164795,4.140489266731448,4.1256030176483645,4.06785094123491,4.02306994932305,3.996010958206078,3.9601860924020933,3.9243744823388678,3.896705176252473,3.851820215009093,3.794769167155822,3.7794295056615095,3.767957614907557,3.7115250096397663,3.7091760999559007,3.6514760577057856,3.643029327341882,3.629352241909551,3.5843144117215413,3.5603254597491887,3.5337340354810536,3.5178437337021773,3.4936872384579853,3.4867641062072057,3.463935316663278,3.448591583883596,3.4440612286913623,3.4389579702272606,3.4158282354279716,3.403777180163953,3.3881969779964756,3.3855187530809,3.3668704876285442,3.3534718118835904,3.3355734557447514,3.3258546277180425,3.3193298944666774,3.298518391417007,3.278118522142152,3.2709216650670543,3.250106652475811,3.229039509067701,3.198241372952377,3.176042218274196,3.1331014661707357,3.118844246526894,3.1107642124368997,3.07945653143953,3.0575851955673166,3.012029853618259,2.9957749857146343,2.9676845409244645,2.9345343733710623,2.91478093081866,2.8764943421300755,2.8584233627536193,2.828191367666866,2.8200873061433427,2.8022676156781925,2.7678073568565953,2.7517499471605973,2.718850283132265,2.717900319133114,2.6847526944393874,2.671397527955503,2.6368506904319213,2.6242036079486395,2.6186610037743483,2.6018673689562384,2.571779408806581,2.5418254221033614,2.5170800257626684,2.4714337651856493,2.456507972137315,2.44571655276978,2.3831990323296584,2.3360805269291527,2.3118979989263515,2.309187186542201,2.306016839939378,2.2242502071258006,2.1934119842955484,2.140599914693106,2.138716219333303,2.136459024559704,2.0574746706237566,2.037567832948964,1.9773199814890958,1.97642729094244,1.975182989446835,1.9076781213384848,1.8596770011005566,1.8431074048819198,1.8097660642005629,1.7849932091114544,1.7697322240226336,1.733840285222116,1.7295229416514628,1.6920622754850134,1.680855714735359,1.6443491389542917,1.64024450338177,1.6373799811491008,1.6333305297175622,1.610663917371495,1.6043387555236048,1.6201236210273535,1.6443491389542917,1.6693663763930582,1.6772892315728498,1.7401066375669565,1.8097660642005629,1.8164477728278863,1.820221954468594,1.8730519858071242,1.890500759744973,1.9563402235076355,1.9657082589477959,1.975182989446835,2.032823588676898,2.0702726173293744,2.099953328348823,2.140599914693106,2.1657464484531275,2.180131114905322,2.231857816353747,2.271286126801466,2.2935458995982607,2.2990831188403247,2.306016839939378,2.3738267017737495,2.429908246991113,2.451012675277889,2.4714337651856493,2.543134246423527,2.630035140541839,2.6368506904319213,2.6377658951905367,2.6396063355302415,2.7493675858899946,2.8022676156781925,2.876038019122209,2.8978282081943547,2.9676845409244645,3.0219135600253217,3.0767155475211023,3.1331014661707357,3.212365552388503,3.217940003226138,3.298518391417007,3.3454196001911845,3.337396214634275,3.430542292323695,3.454108126580447,3.463935316663278,3.4918146639452186,3.5671068872593246,3.629352241909551,3.6815326137627657,3.789165045188456,3.794769167155822,3.797457328389596,3.806498474622215,3.9204153951269873,3.9601860924020933,4.034089209816189,4.0488964265885325,4.1256030176483645,4.190092221187282,4.232980446723847,4.291019942894637,4.338036329821206,4.419670556057456,4.456436868140909,4.483788595721887,4.612197797469374,4.619733575080549,4.62185379338718,4.626417914489041,4.735766444161978,4.787270718633451,4.849663509926472,4.926526213840825,4.952687643879724,4.9617954191082525,4.982606939542018,5.07060103910637,5.118104569125995,5.183755689028683,5.2411336525376235,5.283521494372266,5.300576440238286,5.346530557692322,5.412836925196871,5.448938419618537,5.520627266113072,5.5674851727564985,5.61435534486481,5.6277818100049135,5.651460152849994,5.708767349193508,5.779772270111081,5.782404581840092,5.784226591603199,5.7834961556895355,5.779772270111081,5.7481687292733135,5.739179140380443,5.666094889779483,5.61435534486481,5.5680351062170494,5.49821171671949,5.463879946493144,5.448938419618537,5.416796524215362,5.343102728088812,5.283521494372266,5.215982886338304,5.176137369423097,5.118104569125995,5.082947387539981,4.962897904112317,4.952687643879724,4.946339783586003,4.923614619804697,4.816529283593461,4.787270718633451,4.711384298496657,4.667527550288396,4.62185379338718,4.614192159209271,4.608976787211239,4.604591073407228,4.564380226667431,4.538894513068598,4.535058608335152,4.534639377131471,4.515547786714938,4.515547786714938,4.51971417087541,4.520476177890702,4.524700663421836,4.5293323975174555,4.543251033352668,4.5541741081439575,4.5599588249561585,4.575885600757493,4.583944556238366,4.608134275296392,4.612048882343368,4.613871141532426,4.62185379338718,4.6449298633537435,4.650287642921265,4.65574830062207,4.6737335755957385,4.685449312263534,4.6990325295143105,4.700982075959677,4.717915758125052,4.728971306346393,4.740395242062245,4.749936156116975,4.756221186447199,4.782442424129298,4.78338803467304,4.784071591435964,4.787270718633451,4.815699658372569,4.822501779266597,4.836094577059944,4.849757527441474,4.8655367404127094,4.886079282704845,4.9004386069469845,4.914482571293792,4.924182850726503,4.952687643879724,4.967232090488588,4.972711741602387,4.986617237057729,5.01407605237379,5.038122826353153,5.060943709384402,5.0948994025991166,5.103770312183553,5.107507307141923,5.118104569125995,5.147916944360171,5.157276846245924,5.168759221179249,5.180893279852738,5.195552307709168,5.207073951443967,5.209296056553702,5.219940970096868,5.224949678881707,5.229463735065702,5.232627692452603,5.234231010305573,5.237096793318175,5.237096793318175,5.235535451964623,5.236899529353549,5.236899529353549,5.233267945799479,5.233934880364373,5.233934880364373,5.227094930678671,5.226904669159309,5.226698992706288,5.213338040550161,5.212284795323361,5.209158136784753,5.188156089688306,5.177317168310548,5.169751319748576,5.153762456780825,5.118104569125995,5.072853887569893,4.98866317261426,4.952687643879724,4.926250529338352,4.851131174342081,4.787270718633451,4.74447408171218,4.676501631507396,4.6413675232810405,4.62185379338718,4.544178570121284,4.505632654534082,4.456436868140909,4.450275748414761,4.443706237590655,4.368603065374334,4.291019942894637,4.287550648010715,4.284698206606086,4.261104987661746,4.214624299207953,4.154547445610243,4.141356327816533,4.1256030176483645,4.067222287694971,4.020191472607447,3.9921268707083044,3.9601860924020933,3.9164975739827614,3.880777998194956,3.84307181131933,3.794769167155822,3.7728101918161627,3.7583203770571156,3.7190964223861744,3.714012545230416,3.66833198103234,3.656905732567882,3.629352241909551,3.6103196434569664,3.6034050578161594,3.594773732088452,3.5727468063822556,3.5559504481511546,3.538656793613365,3.5338464363605215,3.515549373487765,3.5051824409166237,3.477344083978144,3.4738259697385523,3.47152562883225,3.463935316663278,3.431852024120527,3.4216299944626023,3.3933846221189174,3.3865251264094525,3.356106150840837,3.3373169379864276,3.298518391417007,3.282549175966154,3.2741969273160345,3.2419180339937945,3.222972396219342,3.1799533873059547,3.162829809105225,3.1331014661707357,3.101879702854304,3.083436915952123,3.043207545966551,3.0268268908665172,2.995213887744864,2.9865051118105175,2.9676845409244645,2.9341775947113593,2.9186739435692326,2.886199988197119,2.885516644792756,2.8536948021891053,2.840028346677549,2.8022676156781925,2.7959342586069864,2.7935732456188553,2.7877767489250385,2.751019005725434,2.7321202149601644,2.7027828575310293,2.67588438845502,2.660035115239494,2.6520867217866675,2.6368506904319213,2.5915904948933592,2.564535361682192,2.5262143579289233,2.4714337651856493,2.45653101022765,2.44378445342071,2.3807831035346103,2.306016839939378,2.3050822024996114,2.3041979194043636,2.2983932226194685,2.2321559055400675,2.1738667147785184,2.1618832708944895,2.140599914693106,2.1022600578806667,2.0806410385444742,2.0547856894258345,2.051797613691556,2.0229496085840584,2.0171609014498557,2.0041306494833204,1.9990347320896351,2.000084217126412,2.0061677320374853,2.0078886715071285,2.019365819170643,2.0348195974479477,2.049781423885112,2.0778731604106637,2.110286649554924,2.1232838136025247,2.1296963219526583,2.140599914693106,2.1820882512068396,2.200305781617315,2.2375967982468277,2.2718304269231497,2.2893488736893293,2.295721759127434,2.306016839939378,2.356016444295525,2.3842674428292385,2.420972797967286,2.4714337651856493,2.492199784380592,2.509575143594448,2.5745521093140864,2.6368506904319213,2.663468663969147,2.705718291108158,2.7672539127675417,2.8022676156781925,2.873827997292148,2.8910876501158835,2.9676845409244645,3.0344150633584857,3.065713085544269,3.1331014661707357,3.2096925675093466,3.2262573391429186,3.298518391417007,3.337396214634275,3.3392588234437337,3.4292904789708025,3.45269335534136,3.463935316663278,3.50432745105649,3.5590094026917853,3.629352241909551,3.6658881918385138,3.7326000780414095,3.7695643642242143,3.794769167155822,3.8696826687614863,3.9132588222743614,3.9601860924020933,3.9738025850837317,4.00185708940392,4.069583877962463,4.1256030176483645,4.164173930496894,4.224918006717132,4.249262711088866,4.291019942894637,4.315894401964945,4.338674660184708,4.338674660184708,4.345879934213391,4.344220261372568,4.33404061580228,4.309436779349687,4.301500121759982,4.299416880247087,4.291019942894637,4.27885206388199,4.278381310608708,4.278381310608708,4.26840866434852,4.268187425801511,4.268187425801511,4.264745217762735,4.265975173234995,4.266635989937125,4.269885291354582,4.271920400049995,4.273588009926188,4.287398407606917,4.287890171527112,4.288363646051749,4.291019942894637,4.31362359156892,4.317702683827095,4.323905451992376,4.344102034982468,4.357595880157545,4.378228687119648,4.381454143943296,4.4046333850197374,4.416663867265786,4.453901604559334,4.454744734276511,4.45514131561106,4.456436868140909,4.491520954111547,4.5013834864445545,4.514366660796632,4.524497823810968,4.541987133976532,4.556024036350104,4.565172971817864,4.577973617410974,4.585379276137267,4.60893663878541,4.611479032926763,4.61317401818933,4.62185379338718,4.640243759812835,4.643845393088554,4.649821177545574,4.667263312669208,4.675868688414198,4.691495254332386,4.695547315365465,4.70907015880168,4.724094095946402,4.736282206836401,4.745426010371121,4.7539816980943765,4.787270718633451,4.787856711188139,4.788026801876676,4.788469557067064,4.82730027930131,4.839816546300407,4.8710162017099865,4.872298291482336,4.898144381730399,4.91257586816276,4.952687643879724,4.956164150223493,4.957333078737044,4.959062179540396,4.989767366235119,4.9991025162721545,5.0085837781844535,5.015187334453083,5.023964675269049,5.029297062966522,5.029561753760591,5.031266873469406,5.025475859681343,5.023760913850836,5.022973732355647,5.013150117487864,5.004518958181661,5.000791333441402,4.991313545620036,4.9626458136472795,4.961404126789725,4.959066457314201,4.952687643879724,4.87581279178608,4.801794567433584,4.787270718633451,4.7857598375063315,4.6564820983448865,4.62185379338718,4.550436386330913,4.473333821859782,4.456436868140909,4.454413566477209,4.452554694578138,4.373056342807644,4.330954794892243,4.292459872062967,4.291698947999059,4.291019942894637,4.211595463424409,4.137124545196363,4.131109309629579,4.1256030176483645,4.0510614054562915,3.981889887990894,3.9714138872156166,3.9601860924020933,3.9008496375869495,3.858337543589453,3.834755770214217,3.794769167155822,3.776574156076766,3.7681784215820606,3.7549309021490433,3.731734382473592,3.7083557924823083,3.690700644331736,3.6734387107156863,3.659753977734754,3.6530384308134956,3.629352241909551,3.6172583525425903,3.6140852283176077,3.6074463763959557,3.579838026049945,3.5652949226622823,3.537695322282085,3.5269946433750334,3.5052166583668853,3.4924154182764724,3.463935316663278,3.4405253613315505,3.429600794954169,3.388610133293813,3.3835645133160437,3.3418483220486435,3.3262616314840567,3.298518391417007,3.2665397077245117,3.2483801496774936,3.2082832833473747,3.1910796168692572,3.1612016747210605,3.152418409379928,3.1331014661707357,3.1009669826092514,3.0865210272293817,3.0568006990211716,3.0534327757033086,3.0250317214888165,3.0106774832172825,2.9708652038993577,2.969974681519087,2.9694249905150976,2.9676845409244645,2.930232169287038,2.9186122519791695,2.8866851712690975,2.8858122806258777,2.8577347800821737,2.8397571106945607,2.8022676156781925,2.785957153349421,2.778001376964336,2.738036897741009,2.724143422304712,2.6770782976089382,2.660204981403009,2.6368506904319213,2.5896263056502677,2.5539518261986016,2.518590161575732,2.4714337651856493,2.447180246806359,2.428279246458075,2.3818834010141288,2.360340944376274,2.3248991510520867,2.319288590735054,2.306016839939378,2.269971296498184,2.254632468140752,2.2449872984887547,2.236971190552106,2.2213104600500637,2.2213104600500637,2.221440278803481,2.222050630818811,2.2343157976229104,2.2388587725511107,2.252154203744694,2.265616051065745,2.306016839939378,2.3068229995698957,2.307042420838515,2.3077091765018745,2.352436506207356,2.370135914512037,2.404247132953917,2.436262971090544,2.4529245568711424,2.4599621685406143,2.4714337651856493,2.5255019491432353,2.5615137946720656,2.5964134974656083,2.6368506904319213,2.680109925545465,2.7337810572204466,2.774486828624336,2.8022676156781925,2.8690956985966967,2.8925067709505345,2.9676845409244645,3.0311111331787695,3.069532421961749,3.1331014661707357,3.213831244965446,3.219276330999815,3.298518391417007,3.3392588234437337,3.342601918513191,3.429021689453217,3.4511780450681915,3.463935316663278,3.535803299611347,3.5486242169077187,3.629352241909551,3.6460926015261865,3.669137653542908,3.7320416677842037,3.794769167155822,3.814957006690708,3.8353854121573203,3.88063313955195,3.8889572152053518,3.935348280575104,3.9413868214218315,3.9601860924020933,3.983447231862346,3.991793331235341,3.994659100214893,4.011744611901161,4.022841157492026,4.026065084348167,4.0302303465152285,4.0401223874446455,4.0441578985124575,4.044289619541729,4.052331664038453,4.05664253308939,4.058475977346838,4.063307585064324,4.0682640915789,4.0730651020808395,4.076322771680408,4.082029580053108,4.093825511884395,4.096412703294735,4.101386943547391,4.1256030176483645,4.129437758939128,4.130192838326074,4.1318644176687584,4.164505452037359,4.175064978525006,4.2009821116460255,4.204693583452974,4.23150780538638,4.2481863974284,4.291019942894637,4.2941593078643585,4.295203338125463,4.297048843823818,4.334402638743697,4.348371896408132,4.371288006919391,4.3723726511778285,4.395616906449225,4.4079714890492205,4.431402653413874,4.4373568456932,4.440867673671844,4.456436868140909,4.469725498473931,4.4723410076125045,4.476200433918505,4.494758740274516,4.501384839109532,4.511820151450564,4.519015247030408,4.528503286679344,4.542821727466562,4.544448595638041,4.554408191958753,4.56445243905536,4.575187505608989,4.579949732680978,4.586129730050933,4.605786026807998,4.606951155827799,4.609173938039165,4.62185379338718,4.634360804749262,4.636664637902671,4.642945107334025,4.661893276099674,4.669168211759915,4.688409912913302,4.692564249946551,4.702999469298353,4.718722417301418,4.727151683389183,4.729891284929931,4.727965315532902,4.733802575531433,4.733802575531435,4.7019367123212135,4.6984663545901775,4.685287357431388,4.656734087467603,4.62185379338718,4.544364196880803,4.5351007078131715,4.456436868140909,4.4154126361804185,4.346131890440063,4.308774467458779,4.291019942894637,4.210946598036282,4.190776494542682,4.1256030176483645,4.119048872925015,4.112961006689636,4.041578038420694,4.022799524698776,3.9684296666142505,3.964797133819502,3.9601860924020933,3.908837670312483,3.8833883428484715,3.8578365100004035,3.831081356754332,3.8162778018469243,3.810462944139468,3.794769167155822,3.770979756486941,3.7642083759106537,3.7503041218453923,3.7331800094063627,3.7154136465529977,3.692452428325751,3.670018871641979,3.6572894732683476,3.648944395288318,3.629352241909551,3.6005895436058974,3.588948124781407,3.546598681798981,3.5465039327212082,3.5087938745547405,3.492995972450089,3.463935316663278,3.435213865941586,3.419987440570681,3.3780971998276037,3.371140078529576,3.3358357011248794,3.3244158739037655,3.298518391417007,3.274549123727316,3.264437931273233,3.2450443495110104,3.231236259054593,3.2104341509525254,3.1932528236260582,3.175214157780882,3.1664250363100592,3.1596735532051907,3.1331014661707357,3.126306997108447,3.124626414296025,3.119979928517922,3.0891346375409547,3.076615596990673,3.042192061389544,3.0281063648052937,3.0035161802797194,2.989566543612212,2.9676845409244645,2.927461486528024,2.904009263940348,2.860155804922644,2.8022676156781925,2.7892737810104657,2.7799560938881065,2.7171518295105095,2.6998698649404984,2.650352403271225,2.644516470723314,2.6368506904319213,2.576365074120808,2.5344078364929628,2.513104145542674,2.4714337651856493,2.4576335816569834,2.4509368222718892,2.4451961799896447,2.4194407397972286,2.404081640596763,2.4024778918278473,2.3999715683701783,2.392806945042741,2.39930204476621,2.4013952968146555,2.4110517762232355,2.423425931535995,2.447526220499074,2.454033397968784,2.458951303788327,2.4714337651856493,2.5051712663568093,2.5181773423940115,2.560497573905198,2.576303446255488,2.6079038904176697,2.6198652016570216,2.6368506904319213,2.697558321649696,2.755501655106541,2.7810199841780374,2.8022676156781925,2.866634944944188,2.8920236604223906,2.9676845409244645,3.0227312348790862,3.0791341796891682,3.1331014661707357,3.2059349559117365,3.221353004961893,3.298518391417007,3.342601918513191,3.3405618192622404,3.4110806069949327,3.441848420071741,3.463935316663278,3.530387869343988,3.602753975685461,3.6145975068668594,3.629352241909551,3.6842024253848624,3.723057185123734,3.74475855590177,3.794769167155822,3.794815589995599,3.7948350238429605,3.7948507537342895,3.8296280705980212,3.8389193968703506,3.8453600536444483,3.8541812390300016,3.8636388709162777,3.8705003891706653,3.87144958274466,3.8770461185329133,3.882215183227048,3.882906610352114,3.882906610352114,3.883600095244704,3.884445696814394,3.884445696814394,3.885967940517567,3.8876837691609616,3.8876837691609616,3.8967507151131944,3.904455459210851,3.904455459210851,3.9176551414177148,3.9538165764730433,3.954607690541387,3.9565276815735153,3.9601860924020933,4.000812966225874,4.015271020259997,4.0522098350786155,4.071087979240913,4.095322529944728,4.105864548372155,4.1256030176483645,4.155021237507997,4.165934255695138,4.188899831129008,4.198406630244474,4.222015496904479,4.238469851505354,4.26596542736106,4.272280224208949,4.276179371607599,4.291019942894637,4.306132933224195,4.309024888491569,4.313560929683263,4.329444018027516,4.3352868336600565,4.344951145051667,4.350945927722407,4.357913442831791,4.370077678658525,4.37058330442799,4.376503007839911,4.385235834579772,4.388453227533189,4.389660323439328,4.39196278819278,4.395644839911082,4.395644839911082,4.389404773282523,4.391166066938904,4.391166066938904,4.3697594653339635,4.3667956700110615,4.365033917166484,4.339507259293901,4.291019942894637,4.266190908409444,4.179134803661084,4.1256030176483645,4.0872797896955415,4.061477764918839,4.021365628510777,3.9601860924020933,3.957335076982563,3.9563284246297705,3.954035883431617,3.9162476025228976,3.901850780078494,3.8711760626122302,3.8627225490937764,3.840818893052923,3.8265320287391766,3.794769167155822,3.778409621890635,3.7726760640509998,3.7516046834742145,3.729284179755579,3.7035360124950145,3.677674408299392,3.629352241909551,3.620650934443134,3.616468818440806,3.602351208935067,3.567703614896681,3.5398795600138904,3.516789186231172,3.470467093036726,3.468177765467855,3.467208801188015,3.463935316663278,3.4334712592668843,3.425777218080503,3.414942398250785,3.4077583573512626,3.4010596461295606,3.388287222398331,3.387780518357534,3.3849460941316565,3.369619906313238,3.363241090798166,3.3590979615634797,3.3416579562076727,3.298518391417007,3.294404586618005,3.2929270269512774,3.280671788401727,3.230068395047515,3.186289479153726,3.159473102395965,3.1331014661707357,3.0814039735342993,3.037885371521188,3.0017240734965096,2.9676845409244645,2.9212386164043203,2.880451014310254,2.842836162475227,2.8022676156781925,2.766929443621959,2.739637161130444,2.699341428616318,2.6368506904319213,2.634697307340052,2.633496614858509,2.6319731443250696,2.589399500137519,2.571535830089374,2.5639263821587432,2.5610106426281494,2.547731621046843,2.5500217905456095,2.5506438473232764,2.5571111458042983,2.5718359687905687,2.5821973817537804,2.5954124120147863,2.607234813024008,2.6368506904319213,2.6568831309931156,2.6665346236946705,2.7238337600346876,2.747011857137255,2.7861454895206945,2.7940419485981396,2.8022676156781925,2.838229077137952,2.8977262363420646,2.9676845409244645,3.0203342235555546,3.083872577844251,3.1331014661707357,3.199519867124933,3.224162328812434,3.298518391417007,3.3405618192622404,3.324696348343946,3.360768649479626,3.4139861907530147,3.463935316663278,3.494721761991366,3.5197960337258802,3.559094396122047,3.590702730555652,3.612431532182301,3.616871532356715,3.629352241909551,3.65649619016777,3.6646187689113674,3.671732018903917,3.681639400007862,3.6889613628943234,3.6930143451551505,3.692412024400184,3.692412024400184,3.684055148025177,3.673955513823225,3.673856155768398,3.6641866481079894,3.629352241909551,3.6270223552130645,3.6250567406342036,3.5280880513852324,3.463935316663278,3.3903549310409318,3.37723739923441,3.298518391417007,3.2650919888531487,3.2152878519637396,3.162367254167992,3.1331014661707357,3.0669345183102594,2.9855575778398507,2.975655905077055,2.9676845409244645,2.8978120088927515,2.8376539068285123,2.823452316442694,2.8022676156781925,2.7653753734937645,2.7474051491533107,2.732687033449875,2.7272891483875714,2.7078851997845,2.7078851997844993,2.7086099248932216,2.7103428940017107,2.7289315621616126,2.73529608903739,2.752654593320816,2.7691637446338655,2.8022676156781925,2.8323313510195725,2.857528682291268,2.9195876243682966,2.9676845409244645,3.0395622861484384,3.0640001640973127,3.1331014661707357,3.2114329177589944,3.225337770657604,3.298518391417007,3.324696348343946,3.1564277941491525,3.2093419550518787,3.2631189380716066,3.298518391417007,3.3435654973007196,3.3764713130739565,3.403213677999217,3.4378218143814614,3.4463587945357244,3.4441942612120098,3.4580649682811107,3.4580649682811107,3.4256220349050768,3.3879439711973003,3.3319260094443504,3.309135046858059,3.298518391417007,3.2864842912482235,3.2454366449145367,3.1596972157488326,3.1331014661707357,3.0639680130598874,2.9861750991201257,2.9783667300633745,2.9676845409244645,2.929175924098266,2.914582101965731,2.9139657745313503,2.9137287167454833,2.9135072042575167,2.929383137178525,2.9676845409244645,2.9887494342493373,3.0212648121839134,3.1072584914704446,3.1331014661707357,3.1564277941491525],\n",
       "\"y\":[1.323889937417435,1.3238253501699337,1.3237159837774626,1.2698462080951098,1.2548840565494523,1.233105318503609,1.2120811911273104,1.185942762928971,1.1529279760828834,1.1495723002655702,1.1170014693084895,1.093872466264108,1.06727667902183,1.0480601756880072,1.0340044330653115,0.9868297338801102,0.9791188820675258,0.9728064931170537,0.9120146668325817,0.9101775884470444,0.9079847977453839,0.8464844465825245,0.841236294826563,0.8321136388636279,0.7920675369581827,0.7722950012060816,0.7458857296140757,0.706034126254766,0.7057207150791887,0.7033537075855993,0.6985683667620033,0.6980468850753936,0.7004745786077824,0.7033537075855993,0.7321739800454332,0.756728292242173,0.7664826032056449,0.7722950012060816,0.7894661258624969,0.8126287250430724,0.841236294826563,0.861171622855815,0.9035915262170922,0.9101775884470444,0.9140202714679657,0.9396914972731012,0.9747509724661385,0.9791188820675258,0.9841650817609042,1.0431499086273006,1.0480601756880072,1.0525222325555137,1.0969432470501403,1.1146901384174037,1.1170014693084895,1.1205806580623432,1.1709035790421418,1.185942762928971,1.214784207659401,1.2233275892312148,1.2548840565494523,1.273439871503966,1.3125642678684977,1.3177943388958027,1.3238253501699337,1.3480326390611252,1.3664900452658464,1.3502175482902552,1.3242372293076925,1.3240431318454013,1.323889937417435,2.5660723565753103,2.5647686353386026,2.550383120606836,2.528796679077647,2.495827341718121,2.4912213943515797,2.484108609077071,2.445618363290825,2.426886048097639,2.3972135784767112,2.3816131508743568,2.3579447544771575,2.3491032791583497,2.3290680391079976,2.3017385763507288,2.289003460856676,2.2568652385952865,2.246160216060891,2.2200621672361947,2.213689852269074,2.2049641962404993,2.174534345616189,2.1511208736157132,2.1367088241545438,2.120854372346909,2.1002600308296,2.082179579995231,2.0646617560970113,2.0470955706525387,2.0300975069249136,2.0132382863747496,1.9972045339901352,1.9839027409917045,1.9675286168872446,1.9442969927542681,1.9399228227156402,1.9376380911947755,1.934283963424686,1.9224958900011262,1.9155739226509616,1.9105177517200054,1.9103375253312795,1.9052481625453423,1.903572521489076,1.9027828682406125,1.900998482299212,1.8996202628711045,1.8983910388599692,1.8972427540368586,1.8951359995700554,1.8916337083042571,1.8904090130025604,1.8881234109835607,1.8786588522707244,1.878261765010302,1.8776758069213941,1.8753556991337867,1.8662457026662476,1.8645283191614426,1.859432766280864,1.852372053350241,1.84696894148242,1.8364098308851395,1.8315473496315104,1.8249625476868334,1.8200237796732819,1.8064144055133053,1.8024399284855481,1.8012998142015362,1.798583093479198,1.787231155424267,1.7820371644088504,1.771645201977155,1.7713842622274032,1.7636878777020288,1.7587557673617824,1.7507995031578196,1.748734633830772,1.7472757789496902,1.7386497452107945,1.73856341347553,1.7384810112413303,1.737473111892823,1.734031058663167,1.7338039308045707,1.733198294656448,1.7305492851499484,1.7302316467496115,1.7288711173486342,1.7250840000425813,1.7241055050124472,1.7201260283618258,1.7151808343010875,1.7114186374304388,1.7009051343818098,1.6988877069998654,1.6906682769619876,1.6848480921906135,1.6685318182723416,1.6668897245380143,1.6663753244182007,1.6656890515098675,1.655335989581571,1.6527535649347436,1.6539133695979982,1.657334913693362,1.6575171280594225,1.6609076980388982,1.6685318182723416,1.684568855569482,1.6937095782660063,1.7144984358850741,1.737473111892823,1.7474519235098902,1.7568481781438314,1.7802282040908568,1.8064144055133053,1.812485571592601,1.8174971777454583,1.8298603244731022,1.8380220974856418,1.8565978968553192,1.8599001612182362,1.8702336596271985,1.871521486541797,1.8707707175881292,1.8643457241131158,1.8630196908449634,1.846028889535059,1.8425569574796428,1.825849312679646,1.8164133580185502,1.8064144055133053,1.7816383818827322,1.7555954822829238,1.7455115374925483,1.737473111892823,1.7060714065909788,1.6828731445126928,1.6685318182723416,1.6666002057860436,1.6639399763450018,1.6300569135432919,1.5995905246518602,1.5939147193801495,1.5879543825881695,1.5637273721040716,1.5561043343994378,1.5378387316189364,1.5352047908110582,1.5306492310313788,1.5095147509567641,1.4968871215567936,1.482116981695444,1.4617079374108974,1.4521741560910102,1.4437563566767442,1.4172494185462337,1.3927666437904151,1.3798600082930261,1.3612240494857564,1.339828929682572,1.3238253501699337,1.2983882110950877,1.2567234819007846,1.255804970997541,1.2548840565494523,1.2348007543624617,1.219719355718349,1.185942762928971,1.183222937088646,1.1790603201924852,1.1734193071790302,1.1589946378872145,1.1458042212034738,1.1390592584367503,1.1281240775737467,1.1244696533054541,1.1212840668793462,1.1170014693084895,1.0948347065629123,1.0789707777852695,1.0480601756880072,1.0187138478607705,1.0096172254262048,0.9791188820675258,0.9636675741015464,0.9511870691434354,0.947099041929532,0.9461887521036112,0.9386784708315212,0.9275658090367043,0.9101775884470444,0.9024863803472019,0.8989344303565399,0.8624315718575519,0.841236294826563,0.8201952137690207,0.7894459217213936,0.7772068313783884,0.7722950012060816,0.7563797601608058,0.7318323095156969,0.7033537075855993,0.687984712290818,0.6655282026309624,0.6481777614702469,0.6344124139651179,0.6128747299459776,0.5924553429027095,0.5842675133971515,0.5654711203446365,0.5634792840884901,0.5626862964896797,0.5626715749089377,0.5564607754482638,0.555481253819146,0.5561479295838079,0.5600213589022967,0.5605019765679686,0.5611289282646923,0.5654711203446365,0.5692372469489864,0.5696983637197444,0.5709875157518485,0.5778610221048504,0.5795297215146813,0.5835456559917582,0.5864712777054035,0.5885283754367987,0.5900881108965996,0.5897377596136031,0.5897377596136031,0.5850124080843071,0.5754893555125613,0.5729482875834413,0.5702065346107488,0.5654711203446365,0.5438180504367023,0.5301782411208769,0.5149764913137376,0.49652982672415513,0.4837545160519734,0.4731116988587192,0.45222045523674614,0.42758853310367373,0.4207733589910654,0.4152778973505087,0.39652356602822936,0.39376590091618047,0.37075689121925803,0.36782946049505627,0.35864723948319144,0.3509388849075976,0.3483832001977363,0.3483832001977363,0.34761611817458116,0.3477594423037682,0.3496995548105599,0.35864723948319144,0.361432407571304,0.36191898652264376,0.36246629216247994,0.37172521051466356,0.37405184255701274,0.37405184255701274,0.37490001379510973,0.3744313628114022,0.37170898596588886,0.3604349728326315,0.35992188272588743,0.35953245566446634,0.35864723948319144,0.3366309332716111,0.3256215180822841,0.31154704410693723,0.28970594586271003,0.2841778420556964,0.28019794009361076,0.2542318769140022,0.24728497337900412,0.2255489788105396,0.2234762287786798,0.22076465224222863,0.1908585972268555,0.16357149696155426,0.15783877325935292,0.15182335862174723,0.12369455749386793,0.11570443374548267,0.08288206500126538,0.06764437274663448,0.02466342911911834,0.013940771380783978,0.005298716645615986,-0.03891472658909567,-0.05500052223969787,-0.07717681998845372,-0.09631993439734465,-0.12394181586017927,-0.1518789126167137,-0.16816715318463027,-0.19288310948066067,-0.20697841672604733,-0.25806911917015585,-0.2618244031011425,-0.264016576041155,-0.27531940104528374,-0.31838494822509933,-0.3307656967216239,-0.3505296746610571,-0.37359940517532886,-0.3997069903421058,-0.4294982929699258,-0.44115030697850477,-0.4686482839625872,-0.48550388171911996,-0.529488409535614,-0.5375895775830686,-0.5426127195487669,-0.5679045508141125,-0.5977623989297145,-0.6065308712035504,-0.6207772256465622,-0.6524086675710445,-0.6754721648240318,-0.7085178169434743,-0.712052778773463,-0.7444134584445137,-0.7646397168175718,-0.7994776112757997,-0.8133547520649951,-0.8223773748291432,-0.8758520430813408,-0.8810513418190418,-0.8822960456854769,-0.8841539268793692,-0.9377739358455601,-0.9512373393059583,-0.970849356036648,-0.9958030635010111,-1.0201786329264397,-1.0546208117527844,-1.054669854817329,-1.0891199265469216,-1.1144494585897493,-1.1357775988543537,-1.158061220167403,-1.1754580181050311,-1.214328799835048,-1.2270025137878848,-1.237555756289868,-1.2907912810596973,-1.2959438074083662,-1.3003991263376835,-1.3443685681058781,-1.3624557312046077,-1.3648851010288476,-1.3682455011703696,-1.4210861615956785,-1.4338263946493295,-1.4535787647057297,-1.4769321527213535,-1.5027676882698109,-1.5309267145775558,-1.5487512987902994,-1.5717089818902927,-1.583661369552393,-1.6259158437783636,-1.637337994115239,-1.6406502755107741,-1.645643656035269,-1.6947784205302967,-1.7095915691312555,-1.7279338884076543,-1.7586446308490364,-1.7785328627517374,-1.7970391952379403,-1.8336868872623016,-1.8474741563722188,-1.8571624089083503,-1.8907114808756982,-1.9107979207773973,-1.9164154499927004,-1.9300760759565623,-1.9598655238946145,-1.985356743613182,-2.0073376277729618,-2.0499232497918207,-2.052696901010929,-2.0542980372336634,-2.060957219591592,-2.0974778245474552,-2.1232393308541453,-2.1434956275814354,-2.186921088272628,-2.189995971313466,-2.1921806244746267,-2.2034355342513434,-2.235436817966666,-2.2611219180951085,-2.2825009119606983,-2.326896765582461,-2.326896765582461,-2.3133458026708804,-2.3180898244420494,-2.3180898244420494,-2.307874016588646,-2.3063483197512284,-2.3063483197512284,-2.3034586103032426,-2.303501422661345,-2.303501422661345,-2.303166353212535,-2.305721194084075,-2.306623083246182,-2.3075058766896612,-2.308370194269916,-2.3048913474802406,-2.3044879219429157,-2.303920831372076,-2.290943269912355,-2.2837790259701967,-2.277400376916836,-2.269865039206238,-2.2611219180951085,-2.2351298324039064,-2.2070523712051813,-2.1980074214207956,-2.1921806244746267,-2.171729438316814,-2.1544957420551425,-2.1232393308541453,-2.1118519316726365,-2.0924985304716337,-2.068606803588796,-2.0542980372336634,-2.025222091687835,-1.9992716476607577,-1.985356743613182,-1.9824844694106765,-1.9779398507144383,-1.9402992401172245,-1.9164154499927004,-1.8963804546123295,-1.8557022646521217,-1.8502287767156322,-1.8474741563722188,-1.8415417032514183,-1.801862096611487,-1.7785328627517374,-1.7501636914762955,-1.733952269053137,-1.7095915691312555,-1.6964827482659373,-1.6432426598667074,-1.6406502755107741,-1.6390477853655314,-1.6299247659962828,-1.5830090267578503,-1.5717089818902927,-1.5520596150562218,-1.5291432610258298,-1.5027676882698109,-1.4787682432077065,-1.4406188909549797,-1.4338263946493295,-1.4316328285989801,-1.4285092885357815,-1.3953586870901193,-1.3648851010288476,-1.360022334756235,-1.3557938514038068,-1.3280915640307716,-1.2991410222950321,-1.2964868528689286,-1.2962290992752012,-1.2959438074083662,-1.2632266324283639,-1.2331782956146657,-1.230011122865792,-1.2270025137878848,-1.1928688076798406,-1.1925083002120784,-1.158061220167403,-1.1554255451650448,-1.1517982565889064,-1.1145064130671858,-1.0891199265469216,-1.0717373029590256,-1.0377501518726309,-1.026306438339088,-1.0201786329264397,-1.005468594348562,-0.9787006638899176,-0.9512373393059583,-0.9297624694624624,-0.8914173837389963,-0.8822960456854769,-0.8782775002435614,-0.8645884941589213,-0.8269331843274315,-0.8133547520649951,-0.7894487614384618,-0.7736112912190372,-0.7444134584445137,-0.7196976358122487,-0.6948985978842592,-0.6754721648240318,-0.6642922966533433,-0.6082683493102161,-0.6069160692516458,-0.6065308712035504,-0.6059268233332022,-0.5524253943460504,-0.5375895775830686,-0.5147315026039831,-0.4961887528813578,-0.4686482839625872,-0.4396764025689821,-0.4261166551348494,-0.3997069903421058,-0.38367032242208676,-0.3361130299007149,-0.3307656967216239,-0.3278378112136471,-0.31785745943026056,-0.2779289917878729,-0.2618244031011425,-0.2286753363142311,-0.22428498021630316,-0.19288310948066067,-0.1821835964849634,-0.15986685045001137,-0.13740903961954842,-0.12394181586017927,-0.09285742147032972,-0.07860481664165953,-0.05500052223969787,-0.04925446507083109,-0.03836620070403729,-0.007636036342362651,0.013940771380783978,0.03360363408159728,0.06440640732011005,0.07323845601862145,0.08288206500126538,0.10472616810129365,0.12244893159280412,0.12986557308455904,0.14262982406898406,0.14545121626628887,0.14619072508888697,0.15182335862174723,0.1538243149387939,0.154041849201088,0.15446080090512604,0.1595820467354998,0.16026073899569804,0.1617241133930949,0.1649253084297686,0.16583830766574126,0.1672577518645979,0.1682028838249905,0.16861984873815627,0.1700288438481441,0.1711365896339525,0.17181744244892405,0.17596584502661594,0.17864756015520955,0.1826495877010017,0.19186895500596401,0.19709325323724736,0.20426987960839282,0.20909450179138878,0.22076465224222863,0.22832535793984965,0.23098641129864683,0.23697303994701846,0.24642682627665868,0.2553887084725175,0.2638895182684302,0.2723868034757708,0.2772642540457615,0.2796110380299166,0.28970594586271003,0.29246597837094557,0.29306759530835125,0.29353404984573706,0.2971187612669266,0.29757929214555245,0.29686277224723456,0.2907851435269202,0.29070940017486224,0.2905629190536705,0.28970594586271003,0.27779001564173056,0.27501433240858697,0.2723170849936287,0.268905233446024,0.26659742945724885,0.27090250275596306,0.280206784716277,0.28188053857395934,0.2850559977819809,0.28970594586271003,0.30961702256686907,0.3201690224299276,0.3389417738400744,0.35864723948319144,0.37151271651147466,0.38206494758634024,0.4064994348646285,0.42758853310367373,0.44355674788258304,0.4621928615979738,0.4820845761715842,0.49652982672415513,0.5236952604787635,0.56213623243787,0.5654711203446365,0.5661154763302831,0.5672700634217587,0.6096067925916198,0.6344124139651179,0.6549077346213079,0.7010353973554415,0.7025325760005336,0.7033537075855993,0.7055512191578583,0.7491449020072705,0.7722950012060816,0.7978622572256353,0.8255046156805705,0.841236294826563,0.8488829504161717,0.8776011238177879,0.901254102802413,0.9101775884470444,0.9261861750945317,0.9565417129629119,0.9791188820675258,1.008903303268824,1.0180931353932254,1.0480601756880072,1.0739992815961021,1.09476339898549,1.1170014693084895,1.131640456263732,1.1725192990643287,1.1828161213044468,1.185942762928971,1.1935145804084608,1.2315109055114246,1.2548840565494523,1.278477319465709,1.3237450403422923,1.3238253501699337,1.323852412183426,1.3239016477027934,1.3698655172923737,1.3927666437904151,1.4140690202313784,1.4481182867181457,1.4563318451332692,1.4617079374108974,1.4935173035435665,1.5293510213006374,1.5299618996024198,1.5306492310313788,1.558579104553051,1.5783025766789884,1.5847125243103632,1.5995905246518602,1.6052474181853262,1.6075540270301967,1.6092217806945217,1.6202657048581472,1.6261757854900423,1.628841141828611,1.6302228862281534,1.6348955096324178,1.6364914879041694,1.6367462959042043,1.638616966231233,1.64073581992518,1.6418373912831181,1.643500465347548,1.6466157231005574,1.6507762467470415,1.6531929571936295,1.655379002184135,1.6638777182862943,1.664682802797524,1.6650636418065772,1.6685318182723416,1.672587142848967,1.673138377140997,1.6732623119475512,1.676109458194437,1.6764904125514888,1.6767251774489913,1.680393971965573,1.6812842063804951,1.6836959069284743,1.6908906006874314,1.6960106729013549,1.7068113931027757,1.7109541018019274,1.7219173324653574,1.7272451167860923,1.737473111892823,1.7533035246220323,1.7640831570824935,1.7841146779529207,1.8064144055133053,1.8187510683058599,1.834804978648553,1.8604670348149805,1.8753556991337867,1.9086822734444877,1.9122727095638177,1.9442969927542681,1.9605128120505673,2.0083675167294834,2.0132382863747496,2.016416780870918,2.0351456419095197,2.0764861955544958,2.082179579995231,2.0898705945496316,2.137356268446313,2.1511208736157132,2.1711949236037644,2.1959855234415957,2.2200621672361947,2.2507652081702925,2.2620901241681186,2.289003460856676,2.3030250546016133,2.3330982909739606,2.349170471935358,2.3579447544771575,2.3883402826046294,2.4253234110770108,2.426041508602142,2.426886048097639,2.4555317008409703,2.4768686526041903,2.483416216812279,2.495827341718121,2.5079508419767715,2.5149897515096034,2.5316529881753778,2.5343977142206895,2.5499729418705894,2.554165104176874,2.5647686353386026,2.575426102981354,2.580871041337159,2.5856991722236917,2.589294688316745,2.593049635327938,2.5852600091052653,2.568113815402865,2.567287453014051,2.5660723565753103,0.9890357785260817,0.9791188820675258,0.9723554792472471,0.9629637911018043,0.968168461999936,0.9791188820675258,1.0074901971230301,1.0463077237605858,0.9890357785260817,1.881489813534151,1.8753556991337867,1.8681873734020287,1.8667304017205972,1.860955857633106,1.8496126346711788,1.8394728545071444,1.8277903828135185,1.8064144055133053,1.8038720676163797,1.8027784769462483,1.7995210775939356,1.782631681076157,1.7721345340564585,1.7628904493520792,1.752541318009874,1.7474501310129607,1.7457886949476502,1.737473111892823,1.7348262964172574,1.7343980511182555,1.7342122025374285,1.7309854320537972,1.7306317693175735,1.7305710585023024,1.7299196206766525,1.7298293102747038,1.729555164098652,1.72806546248512,1.7277939444881816,1.7265799704970326,1.7228167831429642,1.7215457024048946,1.7173363895995135,1.713270992654555,1.7092717481379025,1.6999861113662447,1.697459231561027,1.690513256914349,1.6848540359563668,1.6685318182723416,1.6671880250148123,1.6667579802734944,1.665734775412648,1.6501441120433413,1.6441412376569997,1.6325493137463645,1.6309088915830086,1.6210923447825984,1.6157254559597596,1.5995905246518602,1.5986027970928904,1.5983081258312448,1.5977357258826683,1.5837794055297088,1.5794758769749264,1.5706578374911655,1.5684510992537164,1.5607033083087933,1.5533544538047006,1.542093667672146,1.5393430028454742,1.5370617895360197,1.5306492310313788,1.5186445483267605,1.51421006931094,1.4973489538141318,1.496680409169493,1.4830996484512382,1.4762392781108775,1.4617079374108974,1.4535720496071813,1.4493000128714875,1.440107745550066,1.4330027120817754,1.4220586822993018,1.416308016201231,1.4092424611119125,1.404892576384714,1.4032738572383816,1.3945457043974145,1.3941788359386318,1.3940252050434983,1.3927666437904151,1.387232934758329,1.386642219602368,1.3859360591760779,1.3817693458375406,1.3808728572815272,1.3790808666771812,1.3781356143460077,1.3777951789167937,1.3772428371745176,1.3810702942021282,1.3810702942021282,1.3828179494603812,1.3927666437904151,1.3968731999538089,1.3981353364075475,1.405344668088612,1.418631733014195,1.42990031096581,1.4377086334676608,1.4478085304293118,1.4496471131885094,1.4268242864847518,1.4251463023730175,1.4051267496350452,1.3974497151935679,1.3927666437904151,1.3793717761443962,1.3493337720121557,1.3238253501699337,1.2976551501593092,1.27502103352511,1.2548840565494523,1.2372138563261381,1.2000571118271162,1.185942762928971,1.1557184851850635,1.1490735029522763,1.1170014693084895,1.1050005677843466,1.095971086990779,1.0705173938765138,1.0480601756880072,1.0366260345731093,1.0280453163626198,0.9996567058095152,0.9791188820675258,0.9613436212747746,0.9413081937929868,0.9215613468057753,0.9101775884470444,0.8805341729886584,0.846019450327637,0.841236294826563,0.8404586144964337,0.8395422828985502,0.8013979965904929,0.7722950012060816,0.7630748363618909,0.7529705257040704,0.7290505449366678,0.7033537075855993,0.696158942331428,0.6900286001886777,0.6750024887140937,0.6705073486136963,0.6514404058671928,0.6482222598724916,0.6356672452438583,0.6353058029566108,0.6352619692133001,0.6344124139651179,0.6317186789834159,0.6315703888621118,0.6315460209556876,0.6290403324990472,0.6288185839426004,0.6278059878398987,0.619323800324652,0.6166149199415245,0.607105156257338,0.603204364021876,0.5915281427744001,0.5825365917443137,0.5654711203446365,0.5587732637107723,0.5552653614482996,0.5348312638498869,0.5317355986873245,0.5088631035967546,0.503349261242604,0.49652982672415513,0.4724971628365293,0.45302090404698214,0.441686542055042,0.42758853310367373,0.41118919238959206,0.3983265160196532,0.3835633365587001,0.35864723948319144,0.3578903574998642,0.3574196134341432,0.3562993233474354,0.3367238741813634,0.32711654026665515,0.31428283481432073,0.2926577662488481,0.2914785347264295,0.2905961786961977,0.28970594586271003,0.28705823885711057,0.24497892053761783,0.22076465224222863,0.18844796344670955,0.18426520511208677,0.15182335862174723,0.12338961890386857,0.1132981985135526,0.08288206500126538,0.05593370868165426,0.036941145155257704,0.013940771380783978,0.0016712587897709241,-0.03916660801476324,-0.05101936310359534,-0.05500052223969787,-0.06246477738766831,-0.10174572498888335,-0.12394181586017927,-0.15355972037185106,-0.1673697821415283,-0.19288310948066067,-0.20537760921083326,-0.25028756095804594,-0.25902878251003436,-0.2618244031011425,-0.2665015620136266,-0.3129525350442597,-0.3307656967216239,-0.35891361296467883,-0.36909375581792636,-0.3997069903421058,-0.42614640979114826,-0.44548145353768875,-0.4686482839625872,-0.4846101803704621,-0.5284500551245288,-0.5375895775830686,-0.5441912635091812,-0.5890009761556345,-0.6036529035335687,-0.6065308712035504,-0.6106973467631476,-0.6616981071552326,-0.6754721648240318,-0.6952120933337707,-0.7201222875745454,-0.7444134584445137,-0.7787502918418836,-0.7789782071357738,-0.8133547520649951,-0.838261912586336,-0.8606919877656947,-0.8822960456854769,-0.8985638817923363,-0.9399546103729159,-0.9512373393059583,-0.9603471968441895,-1.0157311253693755,-1.0201786329264397,-1.024101812312935,-1.0879213589501422,-1.0891199265469216,-1.0903065144404436,-1.1569457785289234,-1.158061220167403,-1.159250904497544,-1.223458606293244,-1.2270025137878848,-1.2310566541466663,-1.2882575840070492,-1.2959438074083662,-1.3051340472708928,-1.3523324827103238,-1.3648851010288476,-1.3799338694518708,-1.4168939793475364,-1.4338263946493295,-1.45305723422132,-1.4836025082575426,-1.5027676882698109,-1.5210779118550453,-1.5559759756922018,-1.5717089818902927,-1.58558445174152,-1.6331413394330183,-1.6406502755107741,-1.6470381024409315,-1.6921398435924662,-1.7068655011023184,-1.7095915691312555,-1.713141438269885,-1.7715692260400697,-1.7785328627517374,-1.7848173387761381,-1.8211835406307357,-1.8435476416094403,-1.8474741563722188,-1.8575911912523897,-1.8902650701631494,-1.9164154499927004,-1.9325179376921242,-1.9512308460082406,-1.9659802900857204,-1.985356743613182,-1.9942680635168106,-1.9994930175989385,-2.0028639405278557,-2.0089622691063402,-2.014135163166371,-2.0093061717442198,-2.0039917664797375,-2.0010107250528617,-1.9951664676485938,-1.985356743613182,-1.9687132031727732,-1.9580681502336823,-1.9374602297111545,-1.9164154499927004,-1.9033603679685385,-1.8905941977028888,-1.8673501119167706,-1.8474741563722188,-1.8300388383669062,-1.809266163137559,-1.7914211264351017,-1.7785328627517374,-1.7491471797055764,-1.7242981923331153,-1.7095915691312555,-1.705942884883204,-1.6980164559240443,-1.657092994404283,-1.6406502755107741,-1.610843891455891,-1.6036693754852531,-1.5717089818902927,-1.5484510924986772,-1.5211871038268385,-1.5027676882698109,-1.4909933850973323,-1.4345204928954534,-1.4338263946493295,-1.4334127127757705,-1.4320011624755948,-1.3828213840087984,-1.3648851010288476,-1.3369924373655442,-1.3045811667612157,-1.2959438074083662,-1.294041891533681,-1.2918231761734909,-1.2600578133074598,-1.2270025137878848,-1.2263233709935117,-1.2257534054596015,-1.2193225761229778,-1.1953429963952984,-1.1696965515016826,-1.1643254537882926,-1.158061220167403,-1.1312480919770014,-1.10607326643116,-1.0975498544916613,-1.0891199265469216,-1.061085752331084,-1.0285288356480757,-1.0238944679404174,-1.0201786329264397,-0.9986485403129088,-0.9836905441999435,-0.9512373393059583,-0.9434448597868008,-0.931291997517917,-0.9003407383577784,-0.8822960456854769,-0.8550174826276375,-0.8273474126337725,-0.8133547520649951,-0.8090131062339658,-0.7992736956868685,-0.7608252902944037,-0.7444134584445137,-0.7106096616134265,-0.7096515773805749,-0.6754721648240318,-0.6586491309781808,-0.6103127621167084,-0.6065308712035504,-0.6045278451606286,-0.5958423633213399,-0.5498291622121809,-0.5375895775830686,-0.5186559030807874,-0.49348185054896465,-0.4686482839625872,-0.43615958283716605,-0.43133445007258864,-0.3997069903421058,-0.3792252768607085,-0.3441276410227685,-0.3307656967216239,-0.3227276293676611,-0.29212900530979447,-0.2693449124857663,-0.2618244031011425,-0.24587970940722403,-0.2199181608101064,-0.19288310948066067,-0.17227365481924295,-0.12869996833683706,-0.1256352557914444,-0.12394181586017927,-0.11821173851371158,-0.08246329160572019,-0.05500052223969787,-0.039080480629839265,-0.010484114650699095,0.004680817397714865,0.013940771380783978,0.0439601739753237,0.04960675932714054,0.08288206500126538,0.09411554252257215,0.11817261056583295,0.13970295184328707,0.15182335862174723,0.1851967360829918,0.1895694859959769,0.22076465224222863,0.23013075175482767,0.2480341948126985,0.27112717811806286,0.28970594586271003,0.30838280460765555,0.32922226929395526,0.34040467212401593,0.35864723948319144,0.36622974660328156,0.3705345241318718,0.3789139057589508,0.38613173407278056,0.39549356136911795,0.4044564001395412,0.41880083679384006,0.4214073682401005,0.4231840445909909,0.42758853310367373,0.4439346503079009,0.4511035101654728,0.46418585800635226,0.467074705495214,0.4777983997547275,0.48157960118090104,0.49479662783614176,0.4952008472947411,0.49538774878183167,0.49652982672415513,0.504640208309056,0.5058881348195112,0.5085284997589157,0.5152484755594533,0.518539312733918,0.5301985253213961,0.5305445202308481,0.5399005076790542,0.5481905160967693,0.5654711203446365,0.571423976991627,0.5750824132663284,0.6009315107332331,0.6076360781742838,0.6273241033398738,0.6299075856067122,0.6344124139651179,0.656855777452654,0.6716107235505526,0.6716107235505526,0.6707634430471283,0.6669340076069363,0.6571935492798224,0.6397310816955204,0.6367335700073489,0.6358907035318695,0.6344124139651179,0.614106021365846,0.6048530180384994,0.5954065340859294,0.5912245678389119,0.5810309813735279,0.5791673406788083,0.5726233633264521,0.5713638601354893,0.5725688734986325,0.5794865151094757,0.5815136369348219,0.6006884253330784,0.6026565077489869,0.619174995427842,0.6266703153541511,0.6344124139651179,0.6640739989392039,0.7014481242855068,0.702627894738217,0.7033537075855993,0.7053071618259641,0.750639655529834,0.7722950012060816,0.8031060294522665,0.8126022394697467,0.841236294826563,0.8620586194477773,0.8911922895533366,0.9101775884470444,0.9325545079227431,0.9546771538790915,0.9791188820675258,1.0120932144972392,1.0162515981297617,1.0480601756880072,1.066495792205401,1.1153447595684667,1.1170014693084895,1.1178394634014466,1.120042275520699,1.167513319083811,1.185942762928971,1.2153510582757234,1.2346110629876024,1.2548840565494523,1.2619029424514117,1.2734961919305543,1.301251270274268,1.3238253501699337,1.336940061375175,1.3484893682735613,1.3613340545809218,1.3655327957805885,1.378013769634213,1.3791661383577627,1.3830301862456715,1.3840663139828862,1.3834216613256038,1.3814465628814676,1.3809834307338984,1.3800209172599485,1.37961746694998,1.3794942268956727,1.3800343478191661,1.3828612373610327,1.3828612373610327,1.3838483537480246,1.390208862592679,1.390396658246973,1.390844006467947,1.3927666437904151,1.4019822533046518,1.4036965800328578,1.408266034851907,1.418557533348228,1.4281567079278985,1.4390876829575503,1.461250955516881,1.4615033376847628,1.4615763843370515,1.4617079374108974,1.4845137405110127,1.495877921176635,1.506248668228904,1.5211361472805236,1.525427902606498,1.526704636061671,1.5306492310313788,1.5448615563216612,1.5500948485277406,1.560213661175942,1.5622399118195873,1.5704609669691583,1.5779119671219894,1.5913104524216348,1.5930910555503632,1.595104364007987,1.5995905246518602,1.6210044590033426,1.6348812332465275,1.650625911913369,1.6685318182723416,1.6851867612782443,1.7049765993673858,1.721752361389767,1.737473111892823,1.7589922901023356,1.786281315059807,1.7947486085078102,1.8064144055133053,1.8254086154051792,1.8416535587041127,1.845864490525463,1.8475233390383656,1.8599418537946986,1.8611797265729275,1.865063175490222,1.86893668155319,1.8697361169931699,1.8753556991337867,1.87923010275632,1.8792978174635961,1.8792978174635953,1.887043826380403,1.8873974476794335,1.8869506902564113,1.8851172394586766,1.8833369569334661,1.881489813534151,0.9179119733818868,0.9101775884470444,0.903001595038122,0.88276174496843,0.864172689588901,0.841236294826563,0.8371293517815697,0.8358889071830187,0.8383773246281376,0.841236294826563,0.8473992441405884,0.8964417994365088,0.9101775884470444,0.9209837130305538,0.9441039354253475,0.9464278786856446,0.9480355912713248,0.9480355912713239,0.9179119733818868,1.681399130770949,1.6685318182723416,1.661273541716938,1.6584913485598602,1.653513704327993,1.6446984104886027,1.6377160214708657,1.631730150007725,1.6306631372292952,1.6257761589515956,1.6241918065108796,1.6228331063850177,1.6216788069837462,1.621379720338258,1.6210267344442033,1.6208618582197727,1.6200260123525632,1.6188289262183368,1.618238392518561,1.6161636435798017,1.611041291617767,1.6098854789864183,1.607951980490864,1.5995905246518602,1.595013567503114,1.593957884431528,1.5909546676237318,1.5785033514031404,1.5718084332723294,1.5604923126993309,1.5548393526870377,1.5462961963522983,1.5421007768397064,1.5306492310313788,1.523688061827817,1.521173536121625,1.5164612980203702,1.5064312715777262,1.4984763482915553,1.4896529429151122,1.483630603968623,1.4769334599558541,1.4732968867052914,1.4617079374108974,1.4568184994356064,1.4552792665345886,1.451447353858129,1.4391068471027366,1.4313764744024193,1.419035116032806,1.4044985829540013,1.3996418473046126,1.3971018528493278,1.3927666437904151,1.3694490371886636,1.3534052761811943,1.3401057649618395,1.3238253501699337,1.3072100478051127,1.2900801112626383,1.2735324176821456,1.2548840565494523,1.2394267016563005,1.222137848841681,1.209044389541686,1.185942762928971,1.1838379989852927,1.1823490267459316,1.1823490267459316,1.1785069573978917,1.1781316822688415,1.1791912975851973,1.185942762928971,1.1879398333217863,1.1881720482947737,1.1881720482947737,1.1897068276070804,1.1897512685059275,1.189121941508525,1.185942762928971,1.1751873855522539,1.1722172005782627,1.1475871888047533,1.1170014693084895,1.1167373696540266,1.1161028055176376,1.06210418729917,1.0480601756880072,1.0324497850113983,0.988910620334027,0.9791188820675258,0.9738120518529665,0.962189202159736,0.9293553852925451,0.9101775884470444,0.8906244287839793,0.8705113632382564,0.8604760957807218,0.841236294826563,0.8375581496268008,0.8360774037335692,0.8355261201659503,0.8311170990693326,0.8302770664573669,0.8308761083022538,0.8340360252159296,0.8340360252159296,0.8329068410899043,0.8297493182903213,0.8290109876805283,0.8188191734364989,0.8114754632404515,0.7984377921103829,0.7870119395245614,0.7722950012060816,0.758457754517194,0.7495235807295173,0.7296775766397103,0.7033537075855993,0.7001805678878861,0.6979569551251283,0.6788386112523166,0.6702025377617011,0.6448104985998477,0.6402334677805821,0.6344124139651179,0.6093191961973514,0.5887577670734854,0.5793653530123248,0.5654711203446365,0.5519788657204763,0.543310669496972,0.5331853636048334,0.5322201008242291,0.5227926348536518,0.5231439701353504,0.5227400498768255,0.5227400498768255,0.5242372568892422,0.5237032919907016,0.5237032919907016,0.5147695434665471,0.49652982672415513,0.4904702080399512,0.4855099112903143,0.4428419624595201,0.42758853310367373,0.4068821322905758,0.3839859053363699,0.35864723948319144,0.3285054959336793,0.32053543643794624,0.28970594586271003,0.2601049398968107,0.25005107917304636,0.22076465224222863,0.19883617325491842,0.16990485362669583,0.15182335862174723,0.13999895373921412,0.08455154101399698,0.08322004578142872,0.08288206500126538,0.08230293429002034,0.03096521670399799,0.013940771380783978,-0.0198314295573625,-0.02085373872413454,-0.05500052223969787,-0.07120177623562896,-0.11436164040261598,-0.12120640769710445,-0.12394181586017927,-0.12985993062539203,-0.17059948616564613,-0.19288310948066067,-0.22113497097054724,-0.23982800467809096,-0.2618244031011425,-0.27235034453580553,-0.30791553583967524,-0.32544476629976504,-0.3307656967216239,-0.33951401252760194,-0.38061127926890626,-0.3997069903421058,-0.42856337299777403,-0.43793621131199734,-0.4686482839625872,-0.4967922824548947,-0.5115447343196871,-0.5375895775830686,-0.5573678355717431,-0.5908235866945373,-0.6065308712035504,-0.6191332712031548,-0.6683367567345893,-0.6754721648240318,-0.6813648615043326,-0.7353192161927495,-0.7433676830066007,-0.7444134584445137,-0.7457882233842152,-0.8044626915401993,-0.8133547520649951,-0.8248742929438682,-0.8659074334129495,-0.8822960456854769,-0.9027742041799729,-0.9283514035490996,-0.9512373393059583,-0.9781030030865012,-0.9925214402159259,-1.0201786329264397,-1.0500934861281959,-1.0591268100048348,-1.0891199265469216,-1.1183614244316007,-1.1291944403920997,-1.158061220167403,-1.1845374332095253,-1.2017442770776916,-1.2270025137878848,-1.2486924753163269,-1.27713050745086,-1.2959438074083662,-1.311272537976215,-1.355149896114515,-1.3648851010288476,-1.3725546671350237,-1.4246077361059974,-1.4325225813478468,-1.4338263946493295,-1.43591309172208,-1.490660441767445,-1.5027676882698109,-1.5237547957972652,-1.5464454591173822,-1.5717089818902927,-1.6002540109353003,-1.6188685885482332,-1.6406502755107741,-1.6528895942063686,-1.6807268921804472,-1.6916648171777586,-1.7095915691312555,-1.7158350176036303,-1.7183678769176853,-1.7158538852587077,-1.7095915691312555,-1.6978698152335596,-1.6939838500941948,-1.6687409538142575,-1.6406502755107741,-1.6359537407472668,-1.631447023503719,-1.5940581394243432,-1.5717089818902927,-1.5482848605548662,-1.5102753561150069,-1.5027676882698109,-1.499888055413742,-1.491572624600849,-1.4464867286674568,-1.4338263946493295,-1.411305964302617,-1.3929100632177924,-1.3648851010288476,-1.3417681247812707,-1.3034619844162245,-1.2959438074083662,-1.2930945547617716,-1.2883626265973902,-1.251966590831311,-1.2270025137878848,-1.2132103227721354,-1.1986472781299677,-1.1791166390209487,-1.158061220167403,-1.1465599041672596,-1.1368940519280084,-1.1146918556521213,-1.0891199265469216,-1.0823398832221005,-1.0758982383985152,-1.0476133644872223,-1.0201786329264397,-1.0120334029975044,-1.0022062815636579,-0.9742802891888251,-0.9512373393059583,-0.9358746963549054,-0.9153911355346778,-0.896569663434287,-0.8822960456854769,-0.8567860870244846,-0.8212896488812103,-0.8165213675347966,-0.8133547520649951,-0.8006668421082068,-0.7741275923327424,-0.7444134584445137,-0.731291894085655,-0.706843934072777,-0.6856697145408455,-0.6754721648240318,-0.6523240934056878,-0.6364368041433446,-0.6065308712035504,-0.5860911863836398,-0.5467103681031653,-0.5375895775830686,-0.5328554685196325,-0.5127282942504725,-0.4775458111453954,-0.4686482839625872,-0.4549951575285114,-0.42103487657754224,-0.3997069903421058,-0.36708109369378583,-0.3640853941322977,-0.3307656967216239,-0.30843650121465727,-0.2760722533324973,-0.2618244031011425,-0.2540836552433099,-0.23080798666857083,-0.20352724412469048,-0.19288310948066067,-0.16569551294620632,-0.15591101895708803,-0.12394181586017927,-0.11007921075955762,-0.08440969598011483,-0.0659684738029922,-0.05500052223969787,-0.02241649456363959,-0.013453964362444282,0.013940771380783978,0.020626258435129774,0.03248939139457585,0.06425314145294792,0.08288206500126538,0.10937550269898688,0.14045530566196485,0.15182335862174723,0.1555362730529608,0.16401539033330836,0.20235996297476033,0.22076465224222863,0.24998716515472585,0.26830762917651496,0.28970594586271003,0.29792038023878886,0.3165547903786128,0.34322335660866665,0.35864723948319144,0.3857015409081259,0.4274247525780974,0.4275063655984268,0.42758853310367373,0.46043114063082635,0.4904484804163691,0.4927863457246642,0.49652982672415513,0.5202036428929424,0.5359777183958889,0.5476128616760509,0.5654711203446365,0.5760450118289282,0.5845803642507224,0.6074324681046677,0.6344124139651179,0.6396513426917836,0.6452882978025936,0.6713613198188386,0.693193288082322,0.7013937387278042,0.7019613646685747,0.7033537075855993,0.721670486289772,0.7289932135705457,0.7318703266844149,0.7333971919696292,0.7378159871891232,0.743960105384383,0.7473578032861767,0.7520764660233898,0.7593888800952411,0.7722950012060816,0.7865617736148782,0.7972803096811654,0.8231621290018452,0.841236294826563,0.8682932347379775,0.8935749446139485,0.9101775884470444,0.9167311480502849,0.940760817705367,0.9712183388934039,0.9791188820675258,0.9907151378301973,1.0303442957467568,1.0480601756880072,1.0694725770602056,1.0953481167144896,1.1170014693084895,1.1353081153872462,1.175408742056573,1.185942762928971,1.1922346600749552,1.205567670325053,1.2388293995651067,1.2548840565494523,1.2788621683234838,1.3060345864711596,1.3138742507751382,1.3238253501699337,1.3411609990567306,1.351515585472797,1.3606508456727275,1.3625230521123606,1.3708136864852674,1.3702759879592947,1.3707629038571008,1.3707629038571008,1.3663784270789283,1.3648210366756204,1.3618415870550948,1.362785925327119,1.3630779735196783,1.3632090059216107,1.371910985370301,1.3914075262026944,1.392005048252082,1.3923738653075222,1.3927666437904151,1.4257488354890087,1.4566986516933311,1.459586530717114,1.4617079374108974,1.4835618531770431,1.4976414625791068,1.5306492310313788,1.535746943201009,1.5412912493136415,1.57178641793362,1.5995905246518602,1.60704969546337,1.6137310822409234,1.6368990316967174,1.6524332709378196,1.6653691174094685,1.6665340388202803,1.6685318182723416,1.6914693231255575,1.7044345804737495,1.7122995730127237,1.7207487729701865,1.7276627675484906,1.7288056825905609,1.7366442976569725,1.7368113735608905,1.7367775775167682,1.7325548812822036,1.7322269323739117,1.730224479750349,1.719186205304395,1.7145357644998485,1.7010373207301313,1.6982461060581202,1.686940205552069,1.681399130770949,1.619137678006585,1.5995905246518602,1.599319074917466,1.599216141062421,1.5989131408352244,1.5794745632628975,1.5713532270736192,1.5604902503227236,1.555190279475268,1.5474149202505063,1.5443621453891043,1.5324732420904907,1.532148554124913,1.532019173928735,1.5306492310313788,1.5258091057748504,1.5253233301020193,1.5249043272662397,1.5229641103012743,1.522695501749293,1.521990644528373,1.5190900346411422,1.518401892123546,1.5158182895713623,1.5104923744696523,1.5073305878885654,1.497506790506256,1.496926776453503,1.487506861449822,1.4803911538908703,1.4617079374108974,1.461348799624313,1.4611959294993393,1.4608356976594128,1.4408220819902442,1.4319629648244523,1.4215216829009267,1.4150043669020484,1.4066151203741017,1.4032177108621355,1.3927666437904151,1.38588369895163,1.3834489519245898,1.3789367193781508,1.3684628941359125,1.360200223072718,1.3507538188723172,1.342603012318531,1.3359750338187104,1.3323457203411375,1.3238253501699337,1.3100801937951494,1.3029969974511517,1.2830385255339958,1.2548840565494523,1.2543529014847636,1.2538299589374433,1.2158481214775825,1.185942762928971,1.175479712068808,1.153700567271645,1.1287805931124981,1.1170014693084895,1.0945548722466891,1.0739591293924193,1.0480601756880072,1.0221564759739024,1.0015774256871288,0.9791188820675258,0.965111899054675,0.9372465046592722,0.9207902960240006,0.9101775884470444,0.8847927562900755,0.8601030748154348,0.852654280742088,0.841236294826563,0.8259363503680404,0.8164671984093608,0.802258413658,0.794128443970544,0.7843002367326739,0.7814436076620006,0.7722950012060816,0.7648652092795367,0.7624717570410193,0.761981899590515,0.7556002322011417,0.7530595270712026,0.7530595270712026,0.7509667908793944,0.7502237359887087,0.748556042170994,0.7465885627881046,0.7439943302808856,0.7336607863331843,0.7293526441855112,0.7220129320603657,0.7136982723548733,0.7033537075855993,0.6756321825941485,0.6371206644157419,0.6344124139651179,0.6338263680878558,0.631151361563028,0.5726882258399901,0.5654711203446365,0.5580160716964131,0.503185996832872,0.49652982672415513,0.49150549014689515,0.44048101216520186,0.4289736537347557,0.42758853310367373,0.4261297788976681,0.36904150753973264,0.35864723948319144,0.34567649066584094,0.30920740324941187,0.28970594586271003,0.2633683785489853,0.24976073184219727,0.22076465224222863,0.19156923602460152,0.17879370572027087,0.15182335862174723,0.1343009026020412,0.09114225591477387,0.08288206500126538,0.07775960553027117,0.05714454264977942,0.02367180189829421,0.013940771380783978,-0.004624344279703596,-0.02868131466985746,-0.05500052223969787,-0.08004901530302622,-0.10962770601002392,-0.12394181586017927,-0.13060572849328578,-0.1475250734763045,-0.17967412163356133,-0.19288310948066067,-0.2233790740710604,-0.22903738297912923,-0.2618244031011425,-0.27868683038864983,-0.32594832045027866,-0.32955145498279315,-0.3307656967216239,-0.3329158507270318,-0.38350150872801736,-0.3997069903421058,-0.42528195193276597,-0.43999327170416347,-0.4686482839625872,-0.4987230617136129,-0.508946664618747,-0.5375895775830686,-0.559952747782031,-0.5868883728181951,-0.6065308712035504,-0.6232878325825562,-0.6616932277879704,-0.6754721648240318,-0.6878528594075113,-0.7353362304835351,-0.7444134584445137,-0.7527452976103097,-0.8089787735556571,-0.8133547520649951,-0.817427751084653,-0.8775080449576262,-0.8819827223957937,-0.8822960456854769,-0.8826626327430298,-0.9476329552663061,-0.9512373393059583,-0.955224938453072,-1.0154103432090085,-1.0201786329264397,-1.0249044692848956,-1.0862699452524258,-1.0891199265469216,-1.0917842079442028,-1.1300092983743943,-1.155630524969781,-1.158061220167403,-1.1614923423736978,-1.2155851807877887,-1.2270025137878848,-1.244864469847498,-1.2724563928885124,-1.2959438074083662,-1.3264660443815193,-1.3382932173266355,-1.3648851010288476,-1.378292254141404,-1.4091892602871168,-1.4130106587807956,-1.419151628558312,-1.4231797003882658,-1.387964317983109,-1.3648851010288476,-1.346806046512771,-1.3209832827840269,-1.303223821695795,-1.2959438074083662,-1.2699679295495678,-1.2590130278358869,-1.2270025137878848,-1.2166955609448884,-1.2048793374621298,-1.179279766383221,-1.158061220167403,-1.143944437453123,-1.131503747141498,-1.111958719789238,-1.0891199265469216,-1.0806230249322102,-1.0740103165744612,-1.0490688718672057,-1.0201786329264397,-1.0169945257045963,-1.014014995735522,-0.9813004835256538,-0.9512373393059583,-0.9450331539276084,-0.9374069240104825,-0.9063655467433933,-0.8822960456854769,-0.8673652120441804,-0.8475974716569352,-0.8282800610726158,-0.8133547520649951,-0.7895774207214652,-0.7593552342535439,-0.7508066138338045,-0.7444134584445137,-0.7101660747547109,-0.7087405865849856,-0.6754721648240318,-0.6697719261014283,-0.6605420053350546,-0.6253014188388559,-0.6065308712035504,-0.5774406559115808,-0.5600571455309131,-0.5375895775830686,-0.5280751564885833,-0.49670168145871063,-0.4750431361533374,-0.4686482839625872,-0.45823840255569737,-0.4197567186738951,-0.3997069903421058,-0.3681413023897888,-0.36344759627085876,-0.3307656967216239,-0.3078625996522275,-0.27726795016346095,-0.2618244031011425,-0.25315073237310326,-0.22548490790883857,-0.20138522240171408,-0.19288310948066067,-0.1727064080696401,-0.1528987319758377,-0.12394181586017927,-0.1060452735647548,-0.07142724430383529,-0.06094254518695319,-0.05500052223969787,-0.03264276658047738,-0.01753236461810559,0.013940771380783978,0.025648107853915914,0.04587984955666702,0.0690659731384482,0.08288206500126538,0.11381775392903304,0.1284191643904693,0.15182335862174723,0.1592501229069314,0.1755805320894681,0.20640254982664752,0.22076465224222863,0.2549398612705551,0.25592665609655674,0.28970594586271003,0.30410413193603025,0.3413490285466074,0.35337627808897976,0.35864723948319144,0.3732273402442483,0.40046858557644915,0.42758853310367373,0.4466126580439247,0.48170525273574816,0.49030916049225715,0.49652982672415513,0.5286972737972335,0.5529413899739954,0.5654711203446365,0.5667924349301816,0.5683377374498373,0.600334296307167,0.6124017739308729,0.6329721741119756,0.6336273407647881,0.6344124139651179,0.6687093575583742,0.6773533946977559,0.7033537075855993,0.7038722987432657,0.7045951514221795,0.7441608007538547,0.7722950012060816,0.7861907688501222,0.8141518318075796,0.830911639873793,0.841236294826563,0.8728801028233799,0.8767344285984024,0.9101775884470444,0.9253925403405945,0.9749568809724294,0.9774081811474784,0.9791188820675258,0.983711139924742,1.0340210877993097,1.0480601756880072,1.0581567153378821,1.0736521848577198,1.1065749624122225,1.1170014693084895,1.1460336313912518,1.1782279528952135,1.183158007767569,1.185942762928971,1.2123186207622916,1.2212360223921208,1.2548840565494523,1.2588328675694656,1.2628266526533545,1.2998023097823554,1.3238253501699337,1.3407657463214133,1.3639649639690714,1.382286249689837,1.3927666437904151,1.4236741159974682,1.4472331169623565,1.4617079374108974,1.46459772454399,1.4682163239059727,1.5023879174558314,1.5306492310313788,1.539160188137402,1.5473955697313246,1.5697077062982303,1.5967499880776388,1.5990194152709436,1.5992090920995827,1.5995905246518602,1.6216378241088578,1.6322636396330243,1.6377863124133527,1.6394175910623603,1.646477569772601,1.645930632069558,1.6450316947638348,1.644106775648527,1.6354966942464135,1.6349489287859043,1.6270310084023403,1.619137678006585,1.5468524546238647,1.5306492310313788,1.5265535244042838,1.5248455735161701,1.5190298742814572,1.5047070533185267,1.4928661349449261,1.4834553029347242,1.4640435836421513,1.46316139938908,1.4628282901960845,1.4617079374108974,1.4451325880973225,1.4393457989455585,1.4309071199641408,1.429738708089236,1.4236859236088173,1.419643996938579,1.4169559336175488,1.4148221876660148,1.4123618002791072,1.4080898467390495,1.4065942381294447,1.4041661029411654,1.3927666437904151,1.391882994232795,1.3916343762313912,1.3908644417483065,1.3713010573411375,1.362086503445337,1.34982897548173,1.3347287255479858,1.3292824179014837,1.3276212241733014,1.3238253501699337,1.3040271656358144,1.2933391347563927,1.2822456649639862,1.2725501608220955,1.264630101794301,1.2619920960011606,1.2548840565494523,1.239837931593636,1.231645843614713,1.2158207322367374,1.2054769810420862,1.194711560751545,1.1915385499025892,1.185942762928971,1.1563498352754693,1.1196835242041527,1.1180985455329453,1.1170014693084895,1.1154494546721936,1.1075370220911256,1.0612316754308524,1.0480601756880072,1.0264965348910216,1.0112306882501172,0.9984239028109099,0.9791188820675258,0.9728916584030372,0.9701815089081607,0.9657230107247954,0.9542870377939878,0.945041084785998,0.9383258507863173,0.934364087615402,0.9278750295127938,0.9248301493925548,0.914432948335937,0.9135622093358493,0.9128232046663007,0.9101775884470444,0.8979834111292218,0.8946516372205751,0.8728636991243337,0.8602718794899169,0.8491203655097483,0.8444294564131751,0.841236294826563,0.8340416607523644,0.7962484269679462,0.7722950012060816,0.7395275896028548,0.7359463949792882,0.7033537075855993,0.6787178779235421,0.6607846796860328,0.6344124139651179,0.6059619132252192,0.5958520023909384,0.5654711203446365,0.5372640608460499,0.5223259729521224,0.49652982672415513,0.4807302835678917,0.433306456608904,0.42758853310367373,0.4242615800450955,0.4096874139971374,0.3682647203594871,0.35864723948319144,0.3445209270038414,0.3113280337650335,0.28970594586271003,0.25753993926648944,0.2537431769874643,0.22076465224222863,0.19646703641845642,0.17135978749130976,0.15182335862174723,0.1388827546778395,0.0848943673615068,0.08288206500126538,0.08154875544347417,0.0753087076517569,0.02578918337946856,0.013940771380783978,-0.0064076902681944325,-0.02895771297439964,-0.05500052223969787,-0.08276108288667983,-0.10216583259120915,-0.12394181586017927,-0.13582184150714127,-0.17073193621840188,-0.1868213781148027,-0.19288310948066067,-0.20702404483069126,-0.23623937733317701,-0.2618244031011425,-0.28564750106513515,-0.32109441189596355,-0.3307656967216239,-0.3351823484574088,-0.3477069614306454,-0.38728199990365164,-0.3997069903421058,-0.4208184771820864,-0.4424796501555006,-0.4686482839625872,-0.5005095490401348,-0.5066544257227621,-0.5375895775830686,-0.5620007236831888,-0.5840010614439337,-0.6065308712035504,-0.6270738097793851,-0.656123606979373,-0.6754721648240318,-0.695471447451157,-0.7249826863228943,-0.7444134584445137,-0.7653577762189472,-0.7926883945512513,-0.8133547520649951,-0.8368718153268309,-0.8586996865761845,-0.8822960456854769,-0.9115466081055295,-0.9215478128057364,-0.9512373393059583,-0.9804329155171434,-0.9955004255402451,-1.0201786329264397,-1.0350398745982816,-1.068182974705818,-1.070260668227124,-1.074126300677336,-1.0813218632464112,-1.0781016533359944,-1.0625046184628681,-1.04924526932774,-1.0380151119177277,-1.0201786329264397,-1.0120458388955966,-1.0075288281043218,-0.9836102682927472,-0.9717408104566454,-0.9562132893888089,-0.9538051271150891,-0.9512373393059583,-0.9189027954320261,-0.8855005461838763,-0.8837419538166573,-0.8822960456854769,-0.8698283026822513,-0.845194386944486,-0.8133547520649951,-0.8067891991133775,-0.7989483782148126,-0.7687449652688776,-0.7444134584445137,-0.7311014072599278,-0.7159507460385135,-0.6936803558643798,-0.6754721648240318,-0.6553409311611871,-0.6295522769173534,-0.6156827772992686,-0.6065308712035504,-0.5749925210107567,-0.5712467500620573,-0.5375895775830686,-0.5261060290470461,-0.49841436381711723,-0.47658055544162004,-0.4686482839625872,-0.4542368977336033,-0.42329860253893825,-0.3997069903421058,-0.36856510280851396,-0.3599027576554352,-0.3307656967216239,-0.3135750126370498,-0.2674128141006009,-0.2618244031011425,-0.25866096659588145,-0.2482227439238205,-0.20625455673860404,-0.19288310948066067,-0.16347949107540716,-0.15620428626676608,-0.12394181586017927,-0.10777163262706635,-0.07438121802762021,-0.061656058664685265,-0.05500052223969787,-0.031411026459090774,-0.01754475302380598,0.013940771380783978,0.02633073943299946,0.04784103447098165,0.06986967978770453,0.08288206500126538,0.11435800773176918,0.12717442921691147,0.15182335862174723,0.15966726275446375,0.17661875569286556,0.20679986469848588,0.22076465224222863,0.2547252065612384,0.25546059252320363,0.28970594586271003,0.3054435956786219,0.3489270841923928,0.356007667814215,0.35864723948319144,0.3646866402165636,0.4062295007003409,0.42758853310367373,0.45506727437665395,0.4802616387349432,0.49652982672415513,0.502879791878414,0.5150518451072874,0.5466078968546646,0.5654711203446365,0.5883021875005237,0.6209396257005708,0.6282013493852143,0.6344124139651179,0.6655729673592243,0.702552463085095,0.7029641760182126,0.7033537075855993,0.7065310247755998,0.7415117644972322,0.7722950012060816,0.7811653275461725,0.7969195895885144,0.8252572810591476,0.841236294826563,0.8744125438957853,0.87824668840272,0.9101775884470444,0.927672845070068,0.9670542815000203,0.9791188820675258,0.9894970392386395,1.0351465742925225,1.0480601756880072,1.066474382290131,1.0921465465331246,1.1170014693084895,1.1431442813478703,1.1733090151466592,1.185942762928971,1.1904870850261093,1.198214082750423,1.2375928417287185,1.2548840565494523,1.2833996765613045,1.3095773792680814,1.3238253501699337,1.3281160609786746,1.3350474917953261,1.3719281630866234,1.3927666437904151,1.4137974080377584,1.4427096117549296,1.4530532231214388,1.4617079374108974,1.4876722984736461,1.5125663949573105,1.519555580690096,1.5306492310313788,1.5452419939515551,1.5535452604458935,1.5604736596567848,1.5625727402598835,1.5718882838224366,1.5717790505011782,1.571504873026663,1.5709145361708035,1.5625703273656257,1.560765680208124,1.5536154453799438,1.5468524546238647,1.4786874459007229,1.4617079374108974,1.4570225924547464,1.45477190899418,1.4448735899400167,1.432390947475373,1.416333281542752,1.4079938380331192,1.3927666437904151,1.3822619646775167,1.3750991490453965,1.3550472683783963,1.3433833651908702,1.3322547379413225,1.3295003354753878,1.3238253501699337,1.3004780901981818,1.2811667741668589,1.2709593682138505,1.2548840565494523,1.237480773454847,1.2076298081169115,1.1963097636688507,1.185942762928971,1.166081567635898,1.139865627639884,1.1170014693084895,1.09907161818678,1.0557358142462605,1.0480601756880072,1.0445605596561776,1.0304546307972253,0.9841901244358655,0.9791188820675258,0.9738514424866715,0.9196013568495922,0.9101775884470444,0.9006616138110242,0.852186888530436,0.841236294826563,0.8310737237476418,0.7811033514714505,0.7722950012060816,0.7650298437419267,0.7048630653931887,0.7033537075855993,0.7022466350153898,0.6960357129486723,0.6438330024437628,0.6344124139651179,0.6207066245775388,0.5875942984364086,0.5654711203446365,0.5328760690021981,0.5277805950338368,0.49652982672415513,0.4799535173324938,0.4286451622891234,0.42758853310367373,0.4270485819032257,0.4252846684690996,0.3732693361562318,0.35864723948319144,0.33450367110948376,0.31807190854732914,0.28970594586271003,0.26226988632949544,0.24438768329931504,0.22076465224222863,0.20556306147606174,0.15720687875921824,0.15182335862174723,0.1482058634374792,0.12968119205995965,0.09054650485912319,0.08288206500126538,0.07122601686598529,0.03286622896214375,0.013940771380783978,-0.015083903089708084,-0.024287058493055902,-0.05500052223969787,-0.08133082724406071,-0.10269118532259425,-0.12394181586017927,-0.13781577788616772,-0.19179748242945527,-0.19263888365726345,-0.19288310948066067,-0.19338275286559314,-0.24514116653757334,-0.2618244031011425,-0.29586284787727024,-0.2972615922332986,-0.3307656967216239,-0.34748319829061414,-0.39394886741112956,-0.39825807666980495,-0.3997069903421058,-0.40236372413172505,-0.4531944601022806,-0.4686482839625872,-0.49194427862344314,-0.5115413995469194,-0.5375895775830686,-0.5695183082585689,-0.5744918245750403,-0.6065308712035504,-0.6368670278587389,-0.6458507511364582,-0.6754721648240318,-0.7006712860133155,-0.7228115706527687,-0.7444134584445137,-0.760511687989466,-0.8092044566532919,-0.8133547520649951,-0.8160132687148596,-0.8232675798565725,-0.8502566897227868,-0.8762428989283437,-0.8816822619511111,-0.8816663513585188,-0.8678639061924072,-0.8641667864603142,-0.8431195927676574,-0.8203969446694717,-0.8151158585187281,-0.8141980093911254,-0.8133547520649951,-0.779164202787467,-0.7610572229997943,-0.7444134584445137,-0.744130467509915,-0.7438779425889512,-0.7085741364128446,-0.6754721648240318,-0.6731772914809819,-0.6710765852748093,-0.6375977959781887,-0.6065308712035504,-0.6018514304643561,-0.5968361768777277,-0.562319404641086,-0.5375895775830686,-0.5209242445874867,-0.49266555323605,-0.47623147171294367,-0.4686482839625872,-0.4520447742487299,-0.42597818110817487,-0.3997069903421058,-0.3741386380212135,-0.34913974270349124,-0.3307656967216239,-0.32089393479916106,-0.28607556178324467,-0.26686480858939543,-0.2618244031011425,-0.252694631742286,-0.21351929340732312,-0.19288310948066067,-0.16214193715356195,-0.15022323507935864,-0.12394181586017927,-0.11207208097825472,-0.08566438506978713,-0.06475715749188993,-0.05500052223969787,-0.02360702622373889,-0.019555602365896263,0.013940771380783978,0.025503402330418812,0.04608409230518795,0.06955421587845922,0.08288206500126538,0.11421580987156466,0.12765963592572627,0.15182335862174723,0.15987413729298927,0.17758013026280972,0.20737186995434298,0.22076465224222863,0.25256474515106886,0.2565021937454648,0.28970594586271003,0.3076242396153286,0.3573216253132183,0.35864723948319144,0.35937261172718005,0.3616693089915404,0.41197939911696,0.42758853310367373,0.46134687626094584,0.4624076863916948,0.49652982672415513,0.5121544327296115,0.5447369981525729,0.5586733614646451,0.5654711203446365,0.5922407436958692,0.6018523663992128,0.6344124139651179,0.6441458498196346,0.6576178603195593,0.6836718632251659,0.7033537075855993,0.7230072162260996,0.7492160684900271,0.7621867917261445,0.7722950012060816,0.803914128784736,0.8185954796313948,0.841236294826563,0.8467676010523335,0.8598518767137393,0.8951547823442856,0.9101775884470444,0.9356130481523119,0.9503425257150071,0.9791188820675258,1.0127568510809088,1.0143681017347377,1.0480601756880072,1.077943227883995,1.0890118060022371,1.1170014693084895,1.133839423732376,1.1843723576989853,1.1856067774322638,1.185942762928971,1.1866480829661197,1.2355375970672626,1.2548840565494523,1.2828856249086953,1.30916711589937,1.3238253501699337,1.3286064009083867,1.3363997103700158,1.3702324893186364,1.3927666437904151,1.409619770454015,1.4291469606714577,1.4436786600239544,1.4617079374108974,1.473286216927558,1.4811881361544637,1.4895600721287878,1.4930399955167375,1.5042147454825714,1.5042147454825714,1.5041553753666066,1.5045467523907559,1.4953539224001395,1.4947338816797813,1.4863708824367632,1.4786874459007229,1.4111394637472592,1.3927666437904151,1.3874497585592116,1.3843883819450649,1.3628140152612729,1.3591213897345393,1.3358704507452566,1.3308022785944273,1.3238253501699337,1.297682227597567,1.2716124652062537,1.2632978012183584,1.2548840565494523,1.2217285407359832,1.2156290294930892,1.185942762928971,1.1781077360200158,1.1537156191597195,1.1266960821365823,1.1170014693084895,1.1026340534587207,1.069548369995395,1.0480601756880072,1.0206035963784008,1.0083114298195288,0.9791188820675258,0.945174762601249,0.9440668101563872,0.9101775884470444,0.8814367264880096,0.8692130268835245,0.841236294826563,0.8173389836405831,0.7941913812648722,0.7722950012060816,0.7541347727358931,0.7165977111973159,0.7033537075855993,0.6932611038665724,0.6441273211946714,0.6360106302594395,0.6344124139651179,0.6318028320457434,0.5816846012068289,0.5654711203446365,0.5340551558391806,0.5294926321422087,0.49652982672415513,0.4786779652511064,0.432831258398616,0.4288969353837735,0.42758853310367373,0.42507585050756846,0.3767279719603871,0.35864723948319144,0.32519368470311383,0.3236115509888049,0.28970594586271003,0.26950688868997164,0.231198234812362,0.22076465224222863,0.21427583372666215,0.18550037735059588,0.15736169978144998,0.15182335862174723,0.14358643976212937,0.09885358324171323,0.08288206500126538,0.05979981274302304,0.04002174457558727,0.013940771380783978,-0.018997652870270443,-0.022740132573827232,-0.05500052223969787,-0.07892385183436668,-0.10449257121302846,-0.12394181586017927,-0.13883063776346516,-0.18618649961494382,-0.19288310948066067,-0.19816772971714114,-0.22831383212209122,-0.25661181955599277,-0.2618244031011425,-0.2706146914315921,-0.31407832491861987,-0.3307656967216239,-0.3585044844645293,-0.37023678745663746,-0.3997069903421058,-0.42827606549739095,-0.44359229858028915,-0.4686482839625872,-0.49336516950709175,-0.5153055038859535,-0.5375895775830686,-0.5709659689045536,-0.5746008309791324,-0.6065308712035504,-0.6210680329370741,-0.6388264359852389,-0.6388264359852394,-0.6393158287288214,-0.6337530260997841,-0.6236286598181806,-0.6065308712035504,-0.5991312663006885,-0.5956145229996679,-0.5709619786891542,-0.5647521173301318,-0.5432619739774762,-0.5403211675647523,-0.5375895775830686,-0.5036676192317295,-0.49474386646797575,-0.4686482839625872,-0.4667265268039382,-0.46428709890240905,-0.4211076217403611,-0.3997069903421058,-0.3734222302159056,-0.34589963371982657,-0.3307656967216239,-0.32422495558867714,-0.30657208464798247,-0.27173918505915395,-0.2618244031011425,-0.24329257668718585,-0.21855180210036762,-0.19288310948066067,-0.16658466104347758,-0.14089056555290114,-0.12394181586017927,-0.11577633704516588,-0.09660583753184193,-0.06698803576721168,-0.05500052223969787,-0.02054867084061618,-0.02047159116924968,0.013940771380783978,0.026052465516190004,0.04833224494086075,0.07091174234859565,0.08288206500126538,0.11604835671195346,0.12155660661321788,0.15182335862174723,0.16261672780989267,0.18709355080475065,0.21077491074991928,0.22076465224222863,0.24305118440105522,0.2616645756359115,0.28970594586271003,0.31477540226702905,0.34109581037083503,0.35864723948319144,0.36972176557309444,0.4133082289553438,0.4247567824474383,0.42758853310367373,0.4330572345604806,0.4782056435269735,0.49652982672415513,0.5275825429904599,0.5402889408605742,0.5654711203446365,0.574590946324077,0.5888966993232763,0.6176485344568445,0.6344124139651179,0.6585386431639626,0.6903861587967399,0.6979382292737522,0.7033537075855993,0.7368210471521768,0.7460303163375408,0.7722950012060816,0.775489890780483,0.7796865331048362,0.8160275283855722,0.841236294826563,0.8586033805899684,0.8925736945202103,0.9044260457723765,0.9101775884470444,0.9211127032316839,0.9574495974753741,0.9791188820675258,1.0078578222028196,1.0182766678269757,1.0480601756880072,1.078122722851084,1.0878113328970866,1.1170014693084895,1.1370098339350032,1.1759787459124031,1.185942762928971,1.19114511471382,1.204349547192297,1.2408231799444773,1.2548840565494523,1.2867059672606502,1.2985908989040564,1.3238253501699337,1.3309044417875202,1.3409570044874504,1.367465347550279,1.3927666437904151,1.4016220810427469,1.4089954896614354,1.4195932030429623,1.4243000492778637,1.4383269160890753,1.4387659664782828,1.4392158342740076,1.440285140224924,1.4313529118041575,1.4295474945963558,1.4205116096994037,1.4111394637472592,1.3413479120212952,1.3238253501699337,1.3146201299615696,1.3080120962239454,1.2825796804366134,1.2548840565494523,1.2487346826606784,1.241073759493625,1.2088028336168954,1.185942762928971,1.1650996948482875,1.117067034340971,1.1170208170906037,1.1170014693084895,1.1169674662326048,1.0625884223829503,1.0480601756880072,1.0269752646080792,1.0038802242674314,0.9791188820675258,0.9475561601429701,0.9421359085414376,0.9101775884470444,0.8776814255828769,0.8734442895944174,0.841236294826563,0.8093173257767856,0.8038615464273096,0.7722950012060816,0.7413628859257195,0.7335707119658488,0.7033537075855993,0.6769155606723438,0.6576394322449741,0.6344124139651179,0.6166866656754135,0.56812576204609,0.5654711203446365,0.5639463938105052,0.561041132291185,0.5134620072310621,0.49652982672415513,0.4659415363073811,0.45030892440574055,0.42758853310367373,0.4193620737860182,0.4039591682028667,0.37090795663843634,0.35864723948319144,0.3322668422117929,0.320048519484772,0.28970594586271003,0.2678044912512312,0.23120669563862029,0.22076465224222863,0.2145795041319487,0.19103817007433355,0.15812204360964932,0.15182335862174723,0.1424288859196552,0.09889617868332978,0.08288206500126538,0.06040500083338873,0.03891629857884471,0.013940771380783978,-0.019008351365599196,-0.02184066836901799,-0.05500052223969787,-0.08467518433072652,-0.09560807599922905,-0.12394181586017927,-0.15081286590537113,-0.16754663885205145,-0.19288310948066067,-0.2208202708488085,-0.23462130121896152,-0.2618244031011425,-0.29464090315362723,-0.2991844262762853,-0.3307656967216239,-0.35097389676992163,-0.3893589213388382,-0.3893589213388382,-0.3773963920037722,-0.3704607938189035,-0.3467377800307947,-0.3307656967216239,-0.3052677233059402,-0.2663778928213807,-0.2630126290995509,-0.2618244031011425,-0.2592611625994241,-0.21119548185423964,-0.19288310948066067,-0.16103878516833703,-0.1522629447272199,-0.12394181586017927,-0.11070391554626235,-0.08127313310923512,-0.061818737558025916,-0.05500052223969787,-0.03701073468295357,-0.013351597506936486,0.013940771380783978,0.034080141378745044,0.07171036650579632,0.07925559575072594,0.08288206500126538,0.0941353641396625,0.1261298808239566,0.15182335862174723,0.17385141974931217,0.21804238478286964,0.22076465224222863,0.22212895191982218,0.2267380112779711,0.27700935195184373,0.28970594586271003,0.31012486713434795,0.33523420456630193,0.35864723948319144,0.3901753160133601,0.39584927605492615,0.42758853310367373,0.4572217185109362,0.469555158833892,0.49652982672415513,0.5145092287621584,0.5589830441820323,0.5637565979393675,0.5654711203446365,0.5729091010517062,0.6058843096553299,0.6344124139651179,0.6454033975875579,0.6562120994665137,0.6818075930390672,0.7033537075855993,0.7175404626970221,0.7308948094457839,0.7529375979956741,0.7722950012060816,0.789202872588207,0.8074384295010009,0.826508301955744,0.841236294826563,0.8672807417494952,0.9076705451423943,0.9092801167053044,0.9101775884470444,0.9122104175411603,0.9593425113130984,0.9791188820675258,1.00951175837838,1.0164520981225045,1.0480601756880072,1.0808135358615734,1.083988852720298,1.1170014693084895,1.1440978441664869,1.1631647443235527,1.185942762928971,1.1982858583961815,1.229206109020898,1.2465350779633249,1.2548840565494523,1.287573162961357,1.300796246780895,1.3238253501699337,1.3272535853916083,1.3308247457470324,1.3388131131804477,1.3529820764857319,1.3696423114244687,1.3708236822470838,1.3722493766505912,1.3740917118104155,1.3650852534177615,1.3617770510576714,1.3517948948544922,1.3413479120212952,1.265794319886759,1.2548840565494523,1.2340666138945413,1.2145276979766089,1.1987737193969061,1.185942762928971,1.1566611959528736,1.1331095387008463,1.1170014693084895,1.1117998476449684,1.0971782425467809,1.059373038045369,1.0480601756880072,1.030397432622331,1.000910753205679,0.9791188820675258,0.9525862419170807,0.9364591976225145,0.9101775884470444,0.8873788989731808,0.8598257303444625,0.841236294826563,0.8267182579192371,0.7744170226759564,0.7732660348690863,0.7722950012060816,0.7455578791465434,0.7278690817419498,0.7340200191637298,0.7361616576993684,0.7490137447471059,0.7583637820735745,0.7722950012060816,0.7844921888901699,0.7912373944205959,0.8136597032919979,0.841236294826563,0.8445585434766412,0.8472331272999649,0.8810566098069628,0.9101775884470444,0.9190067978734269,0.9321774466953943,0.9637431948640063,0.9791188820675258,1.008118183937905,1.0168111815418484,1.0480601756880072,1.0776654349997261,1.087094164202846,1.1170014693084895,1.147565949883417,1.1580308447532368,1.185942762928971,1.199739559660888,1.227404663164855,1.2423543060271727,1.2548840565494523,1.2749295485183185,1.290465204175438,1.293868652988635,1.2950257992853502,1.299623831621234,1.2875304837250563,1.2853837569615592,1.273711985095622,1.265794319886759,1.1956645445656044,1.185942762928971,1.1711892296768176,1.161477509481435,1.1357758828025042,1.1170014693084895,1.0916943351441737,1.0589435760751784,1.0480601756880072,1.039832638522642,0.9815654842569148,0.9791188820675258,0.9631509440628503,0.9418487227797967,0.9101775884470444,0.9057528540437221,0.9036916914052244,0.905162101477019,0.9101775884470444,0.9212619764441654,0.9247002732728986,0.9503059315014517,0.9791188820675258,0.9835709291409365,0.9896615235464838,1.032010827318238,1.0480601756880072,1.0704487023839548,1.094514143348825,1.1170014693084895,1.1329644568794053,1.1714758838920534,1.1771634859980753,1.185942762928971,1.1967134147482263,1.1999502303465364,1.1956645445656044]\n",
       "}\n",
       "}]\n",
       "};\n",
       "           var plotContainer = document.getElementById(\"zxAKd1\");\n",
       "           window.letsPlotCall(function() {{\n",
       "               LetsPlot.buildPlotFromProcessedSpecs(plotSpec, -1, -1, plotContainer);\n",
       "           }});\n",
       "       })();    \n",
       "   </script>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "letsPlot(data) { x = \"x\"; y = \"y\" } + geomDensity2D() + ggsize(620, 300)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's show the data and the image on the same plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "   <div id=\"8EGlNU\"></div>\n",
       "   <script type=\"text/javascript\" data-lets-plot-script=\"plot\">\n",
       "       (function() {\n",
       "           var plotSpec={\n",
       "\"mapping\":{\n",
       "\"x\":\"x\",\n",
       "\"y\":\"y\"\n",
       "},\n",
       "\"data\":{\n",
       "},\n",
       "\"ggsize\":{\n",
       "\"width\":620.0,\n",
       "\"height\":300.0\n",
       "},\n",
       "\"kind\":\"plot\",\n",
       "\"scales\":[],\n",
       "\"layers\":[{\n",
       "\"ymin\":-1.0,\n",
       "\"mapping\":{\n",
       "},\n",
       "\"stat\":\"identity\",\n",
       "\"xmin\":0.0,\n",
       "\"ymax\":3.0,\n",
       "\"xmax\":8.0,\n",
       "\"show_legend\":false,\n",
       "\"href\":\"\",\n",
       "\"geom\":\"image\",\n",
       "\"data\":{\n",
       "}\n",
       "},{\n",
       "\"mapping\":{\n",
       "},\n",
       "\"stat\":\"density2d\",\n",
       "\"color\":\"yellow\",\n",
       "\"position\":\"identity\",\n",
       "\"geom\":\"density2d\",\n",
       "\"data\":{\n",
       "\"..group..\":[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,2.0,2.0,2.0,2.0,2.0,2.0,2.0,2.0,2.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,3.0,4.0,4.0,4.0,4.0,4.0,4.0,4.0,4.0,4.0,4.0,4.0,4.0,4.0,4.0,4.0,4.0,4.0,4.0,4.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,6.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,7.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,8.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,9.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,10.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,11.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0,12.0],\n",
       "\"x\":[-3.1525867233091436,-3.1525213875261975,-3.15247928075785,-3.1168416835739547,-3.1069434591422684,-3.1004860464757678,-3.090025457441535,-3.077020239651052,-3.0665400573700916,-3.065474834856156,-3.0509841474854875,-3.0428202245347835,-3.033432618962566,-3.0255859118325557,-3.02104995069606,-3.0058260946626953,-3.00358563268912,-3.0024706393967264,-2.991732632111149,-2.991702390577509,-2.992586124039067,-2.999917121248113,-3.0005427141943013,-3.009213560858015,-3.034766756576451,-3.0473835020743327,-3.0893755990032776,-3.1527416931875845,-3.1584210629972036,-3.201313952420966,-3.3066767282092204,-3.3181586184338556,-3.325066766481088,-3.3332595012560837,-3.4144245225039143,-3.4835755436801277,-3.4975217427583267,-3.5058320026976886,-3.524775737272678,-3.5522162085681925,-3.586107275428109,-3.6011598784251517,-3.633189949038149,-3.638392241048058,-3.639772380694286,-3.648992468926399,-3.6594727796091764,-3.66077847655429,-3.661100260840669,-3.6607741056881284,-3.6607741056881284,-3.6596986754469785,-3.648992468926399,-3.6434466888989046,-3.6427244140831383,-3.6404046057250237,-3.6129076288236384,-3.604690059495383,-3.5797906472543044,-3.5732762541400485,-3.549214208955692,-3.5280981468113004,-3.4835755436801277,-3.469104806496339,-3.452418000782842,-3.3762413013462567,-3.3181586184338556,-3.254833490135754,-3.1537299511236214,-3.1527416931875845,-3.1525867233091436,2.639978823761443,2.6433351119727577,2.671367124488312,2.715956928899713,2.784059691573537,2.791216159994555,2.8022676156781925,2.8472137113963676,2.869087939905369,2.896488767950178,2.910894870294155,2.9371086939290976,2.94647040952262,2.9676845409244645,2.9982410265523542,3.0124798858017927,3.055989395448277,3.070482116216647,3.106645827687939,3.117811808939112,3.1331014661707357,3.189279474215943,3.2325042088572014,3.2639382902444414,3.298518391417007,3.3419004114955966,3.3799869160078817,3.421903257006825,3.463935316663278,3.5043871312290023,3.5445085282508018,3.5908810459058405,3.629352241909551,3.685093926330344,3.764180285560405,3.7842738352539076,3.794769167155822,3.8187943114070766,3.9078767840758655,3.9601860924020933,4.041235604176565,4.04412107280649,4.1256030176483645,4.193306127774596,4.225211517441579,4.291019942894637,4.349240050396025,4.401166146206322,4.456436868140909,4.5038974872674835,4.582796530537822,4.62185379338718,4.652488490325801,4.779345172029441,4.787270718633451,4.792837557842747,4.81487952167317,4.930829226006679,4.952687643879724,4.990892940808626,5.062957881026513,5.118104569125995,5.190075238312696,5.223217805246469,5.283521494372266,5.316175665912221,5.40615819539164,5.43940210640381,5.448938419618537,5.467728777171988,5.568327281286145,5.61435534486481,5.696347454007789,5.69840625672018,5.779772270111081,5.830837622150037,5.913214009631661,5.945189195357353,5.9687095988572665,6.1077829205245475,6.110606120603624,6.113024462390269,6.142604304914032,6.267764224004775,6.276023045849895,6.286279991812117,6.424827023026912,6.441439971096168,6.462079495157292,6.577130607768845,6.606856896342439,6.648479283579386,6.718785994158884,6.77227382158871,6.849949973712187,6.86485518613217,6.937690746834981,6.976839821668046,7.086590122339752,7.099167651779432,7.103107672081254,7.109928573058678,7.236862681899593,7.268524597327525,7.303599930333199,7.407075802038774,7.433941522573797,7.452234746569081,7.49336934636842,7.560879370036059,7.599358447820068,7.654483613945498,7.715404846598675,7.74083233039015,7.764775373066341,7.82760623532179,7.897978339197779,7.915625214163812,7.930192298312612,7.986448159208594,8.019770100942798,8.095609223558883,8.132693058598178,8.248736387739255,8.261026148805154,8.272027299345913,8.400025870089697,8.426443074051427,8.496809474453045,8.513163086149502,8.591859999297698,8.615851367782982,8.641274185360652,8.697829626218532,8.75727692454397,8.776564227939339,8.7919391190743,8.847348969157228,8.888283441077984,8.914693879881744,8.91805916161613,8.92269384979024,8.995794543280573,9.061523965946504,9.074492314937526,9.088110775036512,9.167478075847962,9.192451026059784,9.253527700282785,9.264458256585927,9.283363314176889,9.368234803780329,9.418944625529056,9.467913845215438,9.535578402392343,9.561486308535349,9.584361550775327,9.643105231215946,9.697363036831753,9.718810447324524,9.749778476021598,9.788177275592838,9.816899631334765,9.854161830357725,9.915195401267871,9.917405032512335,9.919620445884986,9.96338303921461,9.996238558874857,10.069822417682335,10.074086408532553,10.080612326514142,10.110660958253153,10.18137023897631,10.246029251760413,10.298954450341885,10.384758722168863,10.411446177006685,10.421721791011523,10.435535988364801,10.464632845597825,10.4856127104139,10.526491629026925,10.506449870044495,10.503685737591512,10.494418401143696,10.448519862754964,10.411446177006685,10.3346181509522,10.325041416466483,10.246029251760413,10.20430816075102,10.13902627355718,10.0990665203433,10.080612326514142,10.029756629266716,10.000227418786029,9.965681122518715,9.915195401267871,9.90341001399464,9.898680265363112,9.87700855997134,9.84686418032325,9.81189232924026,9.786654661719279,9.749778476021598,9.716750063880399,9.69054625923619,9.636038815303964,9.584361550775327,9.539261707398678,9.43572823956831,9.423723813904887,9.418944625529056,9.412227429292356,9.275147015353536,9.253527700282785,9.2311577465417,9.101186868242424,9.088110775036512,9.07769217067079,9.005534169349065,8.931730249461086,8.92269384979024,8.909457875836416,8.787005108418214,8.75727692454397,8.713909097295762,8.642247528714087,8.591859999297698,8.532794283061813,8.484668161558927,8.426443074051427,8.3795559391647,8.285063783883412,8.261026148805154,8.249664051772573,8.230040024036699,8.147563343625595,8.095609223558883,8.051348514523514,7.99764006224461,7.960845227775925,7.930192298312612,7.871090755417457,7.801406794573367,7.781127621298461,7.764775373066341,7.690238458154578,7.680512071814853,7.599358447820068,7.577326735228834,7.50822175091268,7.452436857454256,7.433941522573797,7.409314108000558,7.294992539442655,7.268524597327525,7.247055628457172,7.1480420078419105,7.109790371480045,7.103107672081254,7.09394428221162,6.969069875987893,6.937690746834981,6.900729124253047,6.811270536216654,6.77227382158871,6.7409336214264055,6.611146362615765,6.606856896342439,6.604732919097527,6.5999048544556125,6.494265636057554,6.441439971096168,6.38903469806125,6.307710968387511,6.2892871127998475,6.276023045849895,6.195722182448542,6.174238665753398,6.110606120603624,6.104099995904271,6.095588668051503,6.0169454303668335,5.945189195357353,5.930755880558941,5.915610833000796,5.877697282324039,5.8664355916484325,5.8201740598276235,5.816333408845807,5.805500088380747,5.800059982555769,5.800507914121056,5.818368338112219,5.824866342102313,5.832981816876174,5.846047886090263,5.864901109620556,5.878157255527309,5.8858860218846125,5.904524377162858,5.911369081714451,5.936178811468849,5.9389091736162385,5.939929321509595,5.945189195357353,5.974895416998864,5.983435544386307,5.992610650477898,6.007831426697937,6.025056496198564,6.03912522111683,6.044627799566603,6.062113430029672,6.070162998526127,6.091168273720589,6.096159945273824,6.098553653128683,6.110606120603624,6.131645089362026,6.1378236864770574,6.144788655107611,6.165944403375297,6.18136973691594,6.196733698648959,6.198377213447435,6.2186478139446955,6.227492400519591,6.242726398223946,6.250721537665807,6.254374271408288,6.276023045849895,6.2790095735985805,6.279724543601949,6.280480824032276,6.3083269770181865,6.315318844414287,6.323079887041882,6.334509499087604,6.345674305051773,6.358663202728874,6.358682140867657,6.371985148042953,6.380664591227076,6.387972913439132,6.394626381644313,6.399698299699416,6.4110308116007,6.413549810524978,6.416118645742653,6.429077060261635,6.429666735225098,6.430749931504856,6.441439971096168,6.4472689723450305,6.448051892234796,6.4495028754865,6.4720087357360825,6.477435047639544,6.488833574399335,6.503429449797316,6.519576668241731,6.5392924613697225,6.551772502799075,6.570066306544682,6.578178478625183,6.606856896342439,6.614804345182259,6.617109006402584,6.618837954567043,6.642399390051299,6.649502691525667,6.650867240466383,6.654576484954166,6.656978586261147,6.651260771823875,6.639937906923127,6.6368156862480046,6.630102774993317,6.606856896342439,6.59337826312456,6.58960872425882,6.574079751829878,6.54569356497481,6.521403134094733,6.494180644805038,6.441439971096168,6.437598223763672,6.435380511323741,6.425462007636899,6.379628117282925,6.347297052207713,6.324625764852385,6.276023045849895,6.270781214870654,6.267056981308926,6.24901814832886,6.21439452011786,6.186604655019927,6.161902625853042,6.110606120603624,6.103008587169112,5.9853007490726515,5.945189195357353,5.916460391420557,5.833012762692993,5.779772270111081,5.7228710385663515,5.678190111111865,5.61435534486481,5.550623302083876,5.51347442407549,5.448938419618537,5.39269645235677,5.337645297477561,5.283521494372266,5.223124420777305,5.179469617188007,5.118104569125995,5.046551569969177,5.007050840780293,4.952687643879724,4.931709502401549,4.90736893019705,4.849635821897179,4.787270718633451,4.7732899708950125,4.764283510917963,4.738200384234338,4.712274454949098,4.665253114071129,4.64917658442047,4.62185379338718,4.587521508478762,4.566959887060543,4.526201348298416,4.489824124482775,4.467684237831209,4.463328568921259,4.456436868140909,4.399130384346524,4.3627681678467525,4.339091674060407,4.291019942894637,4.284410539393498,4.281084251375086,4.276785684979306,4.235044054848862,4.210502474589838,4.193671671973329,4.184053793174973,4.163269062053136,4.1570561675280615,4.131823154038257,4.1301234004990715,4.129448013566526,4.1256030176483645,4.098489823523719,4.09195938586922,4.078456559059685,4.062317780052913,4.04374285581663,4.017770077287036,3.976483927772179,3.96914550379155,3.965449308862331,3.9601860924020933,3.8870681301074956,3.8198546733543353,3.8064368310879058,3.794769167155822,3.7176342198002086,3.6370236015277104,3.629352241909551,3.6286677159755083,3.6279100556116095,3.5424365196973984,3.463935316663278,3.456716495593934,3.449859082903467,3.3820353055794268,3.3812833998589564,3.3094375745841926,3.304842398872374,3.298518391417007,3.237606355647774,3.1961403826910626,3.174809127800236,3.1331014661707357,3.118398482274788,3.110525423932706,3.0978063734328227,3.0672062896930887,3.0358112577409937,3.0192110898623215,2.989570171664888,2.980157112275128,2.9773265913713765,2.9676845409244645,2.9351046110078363,2.923356350975782,2.9103247895078974,2.8976276059907455,2.8742191805348565,2.861570468439674,2.84887916960428,2.83444549539775,2.8290924592564766,2.8022676156781925,2.801343376033407,2.801080105636948,2.800818270356003,2.7666707322492394,2.7572017025831252,2.7474222206830845,2.736187339995201,2.7195008244018206,2.706365480292291,2.7002177280574307,2.683977529650252,2.6753288819368306,2.6496810184733697,2.645936752448378,2.643875824321471,2.6368506904319213,2.598209530641972,2.582624159563651,2.5509712443176786,2.546779042758561,2.5094143386848202,2.497106050233329,2.4714337651856493,2.43912066763715,2.4197435467624073,2.3806003685197545,2.362652704999797,2.32707967821797,2.3198038616102457,2.306016839939378,2.254245702457667,2.2178952337161286,2.1877787551049694,2.140599914693106,2.1174611532569214,2.0921962147075144,2.0275954722972536,1.975182989446835,1.9224977383000583,1.8318249223681393,1.8097660642005629,1.7962511898616231,1.6933121415802583,1.6491502098964768,1.6443491389542917,1.638020891105727,1.4975483182851548,1.4789322137080196,1.455176459705065,1.3449519520077606,1.3135152884617485,1.2764821877002657,1.187399202434273,1.1480983632154764,1.1044163370941638,1.0290213762389566,0.9826814379692053,0.9247542413767276,0.8816261849056186,0.8172645127229332,0.7479325182294323,0.7086444625286026,0.651847587476662,0.6238463663889595,0.5561149564450991,0.5045717301377808,0.4864306622303909,0.44754044830308537,0.3825872541170927,0.32101373698411884,0.2590701056824267,0.19715215732391744,0.15559681173784767,0.13137520917352852,0.027183750948026386,-0.003197724122965262,-0.009820113508424377,-0.019005220969291692,-0.15745081706970865,-0.17523703875469554,-0.19240904341080967,-0.33806454987814405,-0.3406539640009676,-0.3427101753486612,-0.3547398347722339,-0.477479947083399,-0.5060708892472388,-0.5477935165355117,-0.6215788309191437,-0.6714878144935108,-0.7166045736869777,-0.8141125647348879,-0.836904739739782,-0.8480617702170941,-0.8643994426783057,-0.9545472628276621,-1.0023216649860536,-1.0496027263942502,-1.0992329223518733,-1.136869316679662,-1.1677385902323252,-1.218339523341056,-1.2620125514330174,-1.294841569631568,-1.3331555154785968,-1.3678152789575404,-1.392985003050124,-1.4333920199830454,-1.4905707500891365,-1.4961635499602766,-1.4970263805871453,-1.4985724407248684,-1.5580907555249301,-1.5929632837213226,-1.614813135778149,-1.66398936597114,-1.665959579393184,-1.6670401481519384,-1.669262049270022,-1.7195354404282592,-1.7462327487606175,-1.7680605192477028,-1.7916598861729063,-1.80617374651231,-1.8110589961548413,-1.8294062912174116,-1.8508171972259366,-1.8588948229884186,-1.86781710484884,-1.8835776839767266,-1.8952997381765178,-1.9008706794907244,-1.9013088535856544,-1.9027376915210108,-1.8916442754156013,-1.8827640543671897,-1.877109262072286,-1.8645309035315796,-1.8294062912174116,-1.8219042642504828,-1.819626265345955,-1.811238561831912,-1.7733250288130362,-1.7500028066972373,-1.7205987622151144,-1.6641820604225783,-1.6640899878895943,-1.6640542982465258,-1.66398936597114,-1.6090406736701794,-1.5816629318803197,-1.5496851110310104,-1.4985724407248684,-1.4856731084422332,-1.4772299955834347,-1.4094785326918382,-1.3331555154785968,-1.3315063405700225,-1.3296507668113748,-1.2347531987179954,-1.1677385902323252,-1.1320404920235578,-1.049182355282912,-1.0158947484837726,-1.0023216649860536,-0.9792125430480905,-0.8865125228119082,-0.836904739739782,-0.7667211545351043,-0.7449867408826285,-0.6714878144935108,-0.5946106244228675,-0.582336696013618,-0.5060708892472388,-0.43937749927331016,-0.4047042566757302,-0.3406539640009676,-0.28806874422429374,-0.21783954725814603,-0.17523703875469554,-0.14367832725708585,-0.020987106018295343,-0.009820113508424377,-0.001498611879276801,0.07428258548756883,0.14586651386972527,0.15559681173784767,0.16694710236276222,0.30283203729863395,0.32101373698411884,0.3406727861731387,0.45796875083176314,0.4864306622303909,0.5228151973606394,0.598200189159555,0.651847587476662,0.7254169532175538,0.7536351132811516,0.8172645127229332,0.8418054433196689,0.8889178080378013,0.9446981327318449,0.9826814379692053,1.0361871407657715,1.0957513946738073,1.1184979202911176,1.1480983632154764,1.1838220484453847,1.2045482893268398,1.233551899874711,1.2366766017997035,1.2653832033770671,1.2746072432615918,1.3018284213318951,1.304594554896605,1.305888846327333,1.3135152884617485,1.3271759278111617,1.3290572589658032,1.3319690179002581,1.346541919451373,1.3507661458245748,1.3616807267916844,1.371284503073194,1.3806116957238572,1.4052637001029868,1.414356671687493,1.4296028627318895,1.445288967367036,1.4789322137080196,1.4999851235547155,1.5114785344219515,1.5714184679436558,1.6443491389542917,1.6463755170400205,1.6487586979678444,1.7410340235086768,1.8097660642005629,1.8395451706396369,1.8959924536068087,1.9460940061874226,1.975182989446835,2.0546402819287053,2.0677282854504284,2.140599914693106,2.1660419020625588,2.2303941112992662,2.2804454380147146,2.306016839939378,2.3562373228091182,2.412586243489793,2.4714337651856493,2.5206005252585495,2.6288243049151134,2.6368506904319213,2.639978823761443,9.111905259213012,9.11602538181225,9.10433880384159,9.088110775036512,9.061836466525456,9.006556368933728,9.020036976951,9.088110775036512,9.111905259213012,2.982402662530986,3.0312795617075095,3.1159018701167547,3.1331014661707357,3.1676522757071632,3.2367507867465317,3.298518391417007,3.3498076587551093,3.443654084675586,3.457835261155738,3.463935316663278,3.480475086215815,3.5722882539311804,3.629352241909551,3.69033830105724,3.758614691456817,3.794769167155822,3.8147214788738424,3.914583946465074,3.953835354626955,3.9601860924020933,3.9680102797758554,4.110036555306335,4.1256030176483645,4.142163722993274,4.272896185328786,4.291019942894637,4.310018173267027,4.433864265320546,4.456436868140909,4.482573742883702,4.586687571375933,4.62185379338718,4.670169606905766,4.7292004397251866,4.787270718633451,4.862741777793309,4.883279550264827,4.952687643879724,4.9918509801141,5.1048051312236495,5.114880287463238,5.118104569125995,5.1248157607113995,5.239402249330579,5.283521494372266,5.362602423457611,5.37379350008738,5.448938419618537,5.487652383135167,5.604041442535674,5.611985403031614,5.61435534486481,5.61880572711379,5.741835257726505,5.779772270111081,5.849193017792157,5.870473626025966,5.945189195357353,5.999667838576178,6.08314647456459,6.110606120603624,6.125992337703623,6.169243451884769,6.247219152025584,6.276023045849895,6.355923337501647,6.359935581324141,6.441439971096168,6.476306298257494,6.550158649340851,6.587335743286507,6.606856896342439,6.658684141447784,6.7033988431384355,6.77227382158871,6.82875871236711,6.898158865445515,6.937690746834981,6.962901630620205,7.098839015083655,7.103107672081254,7.106127449079711,7.130865795620595,7.25524708126677,7.268524597327525,7.284913821335392,7.407554735818737,7.433941522573797,7.4667790144569555,7.564252928663366,7.599358447820068,7.636606085972257,7.736711290077835,7.764775373066341,7.788646152679915,7.888280093152709,7.920339075980591,7.930192298312612,7.96037186118148,8.033548834118395,8.095609223558883,8.15319286984488,8.2276760759403,8.261026148805154,8.342743654232985,8.34875170387286,8.426443074051427,8.437679580237148,8.444533966679055,8.458582561196573,8.487647679991278,8.512329922787625,8.529067530640694,8.543543574697294,8.551543591675832,8.549462329687415,8.557994197338179,8.557994197338179,8.519340224433753,8.514906740762175,8.49350851387566,8.455237895355987,8.426443074051427,8.372559490102782,8.325019221738534,8.288461091881079,8.261026148805154,8.21174793721035,8.176097470197833,8.138258974257992,8.095609223558883,8.068295168272742,8.052549028882703,8.00131835907262,7.941668945100211,7.933641872040049,7.932058255307016,7.930192298312612,7.86036291509205,7.807085100397822,7.78689812764048,7.764775373066341,7.703118685181035,7.636881931247128,7.616621482551697,7.599358447820068,7.531332868280966,7.51275268815154,7.433941522573797,7.40080634149208,7.27153542466962,7.268524597327525,7.2664861845040765,7.2269790792160595,7.1095709879649736,7.103107672081254,7.09623008256607,6.950580455623765,6.937690746834981,6.921839366057066,6.808477262858245,6.77227382158871,6.706753110129554,6.6817371225964095,6.606856896342439,6.56591020592562,6.488195630110887,6.457510729156109,6.441439971096168,6.367923061488268,6.3569676578679335,6.276023045849895,6.259660575250344,6.2394237259451195,6.168269810345981,6.110606120603624,6.0767795245193135,6.034705020923077,5.9845375796786975,5.945189195357353,5.8854058064633605,5.784508250816538,5.781588323797941,5.779772270111081,5.774138707879844,5.666958008505601,5.61435534486481,5.555385847934936,5.456020982571914,5.448938419618537,5.446802405477586,5.44464732311183,5.442585542716774,5.390838990406179,5.3610617755878085,5.3610617755878085,5.361362077481795,5.348805483283014,5.351745073455019,5.356501605699737,5.370838073135943,5.384278851909082,5.393751594575294,5.410654213172705,5.419499096094258,5.448938419618537,5.4584907658050685,5.461699252777651,5.466848065216835,5.502195457767961,5.522168854160871,5.543290494768888,5.553138968733638,5.57603562101743,5.584376189857462,5.61435534486481,5.621063123875775,5.6232084081489315,5.625577664690288,5.65709603449859,5.669182795670029,5.681893122479595,5.687808378031107,5.705596449188789,5.716333839514853,5.724186050947797,5.7355134164278425,5.74147348448885,5.757843007924134,5.7615986002643975,5.763932262910888,5.779772270111081,5.786677631730015,5.788033999870274,5.7897692623342945,5.812821581316067,5.819047448707325,5.8271360213142085,5.83805621845214,5.848705046480024,5.862159662412623,5.862254945792884,5.87662657196419,5.8854272487258275,5.893352674075846,5.901455217356592,5.90615634163661,5.918117548881364,5.921491045621204,5.923331110829649,5.934517898280319,5.935374091384238,5.935775965096893,5.942313366428895,5.942397312177286,5.942342110387328,5.942512817870956,5.942512817870956,5.942334680833895,5.936685985592421,5.936374209078991,5.935461738887531,5.926746961754935,5.9255759366667515,5.923138242430598,5.9150705912958905,5.9129249662454395,5.909081358231706,5.904561758169498,5.902491208447991,5.899046946135648,5.899204488907358,5.899204488907358,5.901255861255519,5.907439606199723,5.907439606199723,5.911896556960217,5.927172342864116,5.927691550511986,5.92986231890492,5.945189195357353,5.951730090772534,5.952940965455722,5.953706709420423,5.9618976629953,5.962873890697811,5.960268092867791,5.945189195357353,5.935767962234451,5.934113855459675,5.92091450141703,5.882444283008603,5.851654831096457,5.8184083888169145,5.779772270111081,5.733280636485313,5.672204234308165,5.635737060538132,5.61435534486481,5.572348783467099,5.505577238544625,5.448938419618537,5.391474444766958,5.328234148031608,5.283521494372266,5.259984158441421,5.220476184367291,5.158038883385025,5.118104569125995,5.067609973351866,5.01604496251648,4.984011853418972,4.952687643879724,4.904997511016672,4.86421780604476,4.829104814625422,4.787270718633451,4.756346771049852,4.734012494173131,4.692361454042873,4.657140691312234,4.634638314744786,4.630608403256117,4.62185379338718,4.58240132797471,4.566549643529106,4.550336707702506,4.545168402665583,4.522145098532606,4.512241573112906,4.50063219616956,4.490230974343053,4.4846879920381575,4.458102279270626,4.457720347131895,4.457429451539923,4.456436868140909,4.413400762708605,4.397705129473698,4.357945270485841,4.311744320859761,4.299495221415674,4.295583377369763,4.291019942894637,4.211707447835822,4.129174209009907,4.127232544843878,4.1256030176483645,4.107175865967612,4.036149564319114,3.9601860924020933,3.945155764275439,3.927626109853165,3.859104270090018,3.794769167155822,3.7745424976601356,3.7545376724069346,3.696617108248299,3.629352241909551,3.620436511286359,3.6132878804234885,3.5776931921098267,3.551484405580535,3.4946212326772716,3.4826324999392337,3.463935316663278,3.420639094296206,3.3953972447661656,3.363970253272175,3.33209221583701,3.313579518496878,3.3089356851195406,3.298518391417007,3.2591400360120097,3.242331251854771,3.217409960753808,3.2165087128207315,3.1843569208758513,3.1734664547857436,3.1421756905378517,3.139015860501358,3.1379075031887282,3.1331014661707357,3.1037339514445863,3.095922145850259,3.0876722313057456,3.073516099957116,3.059551434156594,3.0456375464917347,3.043571094065853,3.026797196982174,3.0168281222230506,2.9997450321849684,2.9920374130365612,2.9869709847491857,2.9676845409244645,2.949639919575487,2.9436838016275377,2.9294270312908175,2.9028169582328704,2.875106566138548,2.8517176976546255,2.8022676156781925,2.7982043959181864,2.795959220069169,2.7885189358043583,2.736373771383903,2.696314670978282,2.6750490501463835,2.6368506904319213,2.6146324662681346,2.6010656574828817,2.5648224905803954,2.5570103152056527,2.5109731958887886,2.4983872384063144,2.4714337651856493,2.4423522043860526,2.4259808732445096,2.3860925274527647,2.3808661532030344,2.340246341653229,2.3284897484324167,2.306016839939378,2.261439164154786,2.2255755308577534,2.1854129488646885,2.140599914693106,2.0968289141405974,2.0254224876245486,1.993376367429673,1.975182989446835,1.9265553898722834,1.8757120357395545,1.8097660642005629,1.7542630977146283,1.665434233637499,1.6443491389542917,1.6337810612639991,1.607582155219725,1.518152894168753,1.4789322137080196,1.401326477369313,1.3841895582726655,1.3135152884617485,1.2776438939573573,1.15225698014648,1.1480983632154764,1.1453580748963939,1.1286133025912326,1.0021413917051145,0.9826814379692053,0.9538919636757353,0.8621778175434835,0.8172645127229332,0.7364802351655939,0.7334620411311823,0.651847587476662,0.6103847098460822,0.5239549327929272,0.5007138761253564,0.4864306622303909,0.406096978653542,0.38526056066956205,0.32101373698411884,0.3102049050536957,0.2913575015988936,0.2094471528807027,0.15559681173784767,0.07943307094521579,0.06837658211196374,-0.009820113508424377,-0.06448090038199972,-0.1624754902520955,-0.17523703875469554,-0.1787840292724816,-0.18500503725934347,-0.2919310455552191,-0.3406539640009676,-0.41248064199049317,-0.4442783716532741,-0.5060708892472388,-0.5389334384713091,-0.6543268071996957,-0.6714878144935108,-0.6885180795383534,-0.8032763671583947,-0.836904739739782,-0.917821679553267,-0.9261269188648291,-1.0023216649860536,-1.0208979649062395,-1.0400858777936128,-1.0965689337510538,-1.1677385902323252,-1.1694800970015389,-1.1705514986322516,-1.1724256852530428,-1.219698170750636,-1.2422802510816457,-1.259227898393012,-1.26445130141887,-1.2800443913899828,-1.2831946758360742,-1.287602413658853,-1.2881752280452328,-1.2794645993125884,-1.2745103216867166,-1.2690366949179959,-1.2468568138124976,-1.2440597153494135,-1.2271665923923187,-1.211972790653836,-1.171713680005499,-1.1705141639062684,-1.1697492633565418,-1.1677385902323252,-1.1235192004476309,-1.1063521297507162,-1.0728835813285822,-1.0509644461760854,-1.029358740837842,-1.0191626968783183,-1.0023216649860536,-0.9481576844381854,-0.9041044121248052,-0.8683720228314824,-0.836904739739782,-0.7614857566237063,-0.7368323875908653,-0.6714878144935108,-0.6388549224730999,-0.5294324304261506,-0.5060708892472388,-0.48364864874912517,-0.3678152323665609,-0.3406539640009676,-0.3100720183776966,-0.2067870182842073,-0.17523703875469554,-0.14468731825650316,-0.03358702864470331,-0.009820113508424377,0.01157832623347943,0.14945970175683154,0.15559681173784767,0.16020996500992268,0.18003662406279908,0.29890191241483954,0.32101373698411884,0.35820279274358136,0.42454830659161846,0.4864306622303909,0.5407054334663242,0.6507511105202308,0.651847587476662,0.6521632343675083,0.6527316973625883,0.7625445382565372,0.8172645127229332,0.8758109347741847,0.9598558572317817,0.9826814379692053,0.9921460525269605,1.0213879203760827,1.1139974778584332,1.1480983632154764,1.219034907546856,1.2377169822798422,1.3135152884617485,1.3655305632273533,1.4590651062429227,1.4789322137080196,1.4896962545447865,1.513681261009192,1.5929687979159075,1.6443491389542917,1.6873123590811776,1.7361730194192075,1.7698043907606298,1.8097660642005629,1.8474862471883515,1.8828342441907857,1.9235501275391416,1.975182989446835,2.0031737649292225,2.041738001164709,2.0950254319296624,2.140599914693106,2.2113607721356745,2.239236204016355,2.306016839939378,2.340030500987016,2.44673800558016,2.4714337651856493,2.4849173241682667,2.5796991707831145,2.627554492163136,2.6368506904319213,2.64630936256917,2.7742232612791327,2.8022676156781925,2.8300885003619207,2.9442628164192675,2.9676845409244645,2.982402662530986,-0.48751309743039606,-0.48274829441175005,-0.4888528954592788,-0.5060708892472388,-0.5611042038047929,-0.6290079139181142,-0.6616336638823523,-0.6714878144935108,-0.6783475938036836,-0.6862288697744976,-0.6862751222511347,-0.7044453043320722,-0.7095343904500528,-0.6974159021251753,-0.6714878144935108,-0.593049407282658,-0.5806517698780578,-0.5060708892472388,-0.48751309743039606,3.4948089942217475,3.566502893477473,3.6119368189122447,3.629352241909551,3.665386527041303,3.737583570154559,3.794769167155822,3.871884604446583,3.8856308329632014,3.9601860924020933,4.019214117385756,4.069835041691183,4.1256030176483645,4.177883756299348,4.239586154426677,4.291019942894637,4.340052610601267,4.410276474758993,4.456436868140909,4.496202213855083,4.594378958440812,4.62185379338718,4.641916171721485,4.728676358426236,4.776288821735818,4.787270718633451,4.807991491938392,4.90209132957003,4.952687643879724,5.024292781383545,5.060063077075668,5.118104569125995,5.145581272817665,5.220579906456715,5.26681894724411,5.283521494372266,5.31756385318266,5.390830133884661,5.448938419618537,5.51598933560431,5.5617543577823625,5.61435534486481,5.642161732857275,5.730774500510185,5.768040610410766,5.779772270111081,5.804391393040143,5.89096040634492,5.945189195357353,6.008217457245992,6.082456644408705,6.110606120603624,6.121007969991203,6.1387616275240475,6.220075056109563,6.276023045849895,6.315086080718897,6.36290456067721,6.401573410942017,6.441439971096168,6.486184628433664,6.536609451973533,6.569768701668558,6.606856896342439,6.662286666249273,6.760084949978372,6.767223675853863,6.77227382158871,6.78089658971977,6.919849362911272,6.937690746834981,6.9538901329999945,7.057106453673352,7.098315924979749,7.103107672081254,7.108456593044902,7.259493145018137,7.268524597327525,7.276152680843534,7.314687559876633,7.408135197190438,7.433941522573797,7.507328536507256,7.598461039547772,7.598724770229968,7.599358447820068,7.633055483324364,7.641819440134693,7.63681383474438,7.622852628909522,7.617905369334828,7.612091593527037,7.599358447820068,7.553343468689507,7.526466729832567,7.480857142813228,7.433941522573797,7.387777771517612,7.299271771515452,7.2773498954558615,7.268524597327525,7.254823671722946,7.127387550804459,7.103107672081254,7.078249562959263,6.95496698865446,6.937690746834981,6.917705153966882,6.799835537350258,6.77227382158871,6.718486445424434,6.678264683971827,6.606856896342439,6.571545248448457,6.526062485558231,6.474640897289261,6.441439971096168,6.378278790752102,6.294501389862919,6.283636639744177,6.276023045849895,6.217201813398246,6.19014864573775,6.110606120603624,6.096639152865134,6.07887600595723,6.005397565547348,5.945189195357353,5.9118515376801195,5.862535018056198,5.812145426420775,5.779772270111081,5.702306206904506,5.6941374481808325,5.61435534486481,5.550497683658472,5.511826919329621,5.448938419618537,5.382457539094084,5.3487211858289285,5.283521494372266,5.239757333555982,5.150405602353876,5.132643946591463,5.118104569125995,5.081505670976574,5.0684218756988155,5.0684218756988155,5.057307273700278,5.045782825832788,5.045782825832788,5.044132653746249,5.044857959003533,5.047080265201112,5.047835062420564,5.058493452792604,5.065489635768687,5.074720043676853,5.0836829191773845,5.089733231777684,5.118104569125995,5.118915516216061,5.119121363389574,5.119494128511073,5.158952822059746,5.172037984440001,5.199137188977035,5.200035957986914,5.230056299981655,5.244648396981697,5.283521494372266,5.2900848003949275,5.292707726799685,5.297721349006633,5.336988556832795,5.358466838964912,5.381151237006806,5.396160521169703,5.4162078399113245,5.423682600123341,5.448938419618537,5.46170539719628,5.465580764089497,5.469929025186147,5.494756443117032,5.506292421956843,5.51817608317193,5.5226286038173935,5.537218222560117,5.546826967454871,5.551863655705821,5.561125104345084,5.566899626362858,5.576667472024004,5.580757550058202,5.584117295226024,5.5972347310128185,5.598672282923436,5.60021647808302,5.61435534486481,5.616864566092799,5.61719060109912,5.617653939615783,5.6356908498121445,5.638424326606854,5.64199519512526,5.653677987490264,5.658344087918886,5.663490396369834,5.669267588680881,5.674436897883876,5.678816501073188,5.680715686234407,5.6843586698341735,5.686132690138731,5.686320474272696,5.686943969177971,5.684517049347853,5.683617955144193,5.682378758602294,5.677882057573489,5.674959659555263,5.6716623779825355,5.666397982249828,5.659495754469509,5.655823613633242,5.651134919852488,5.637713880497117,5.635469024724147,5.632757611150103,5.61435534486481,5.6112269906361565,5.610711656510166,5.609348548566571,5.585305360676159,5.579988266748314,5.563999127064264,5.553738346857935,5.542314112548285,5.517429024997719,5.501201141926231,5.491217129977558,5.478305296266946,5.448938419618537,5.40592518281848,5.335428481934063,5.298501950859187,5.283521494372266,5.268495767056706,5.23106690202491,5.146229606914295,5.118104569125995,5.050704127547046,4.975699892656149,4.9639564538931875,4.952687643879724,4.899063339388448,4.8670094801134525,4.843474278567097,4.805284528144471,4.79657278533216,4.794180075680208,4.787270718633451,4.756893662795218,4.748363641034809,4.733235464179373,4.7200279555231734,4.699907172692615,4.677320393026518,4.639892818458906,4.632806720250031,4.628690256518318,4.62185379338718,4.561955281925135,4.520870833483125,4.4895296882842874,4.456436868140909,4.40591674495176,4.351452456899407,4.318616064596425,4.291019942894637,4.22966295837845,4.158993532765775,4.141870973483403,4.1256030176483645,4.05977644693265,3.9959283879730716,3.9797296608428816,3.9601860924020933,3.904897110747486,3.8592757693017976,3.8316301111150253,3.794769167155822,3.760521217398068,3.73454863985922,3.6905605352741997,3.629352241909551,3.6217543021706273,3.6167085106646404,3.5989090206899537,3.5580565001846427,3.51231680240733,3.495419043130788,3.463935316663278,3.4394674363753452,3.427683652546854,3.4083941076386495,3.3921793745605004,3.361657067572539,3.347561129641867,3.320402708412206,3.31254909697077,3.309877356761712,3.298518391417007,3.2771697698350355,3.271770777948255,3.2657592411875944,3.2473445132114485,3.235779614090066,3.220236200533308,3.218571503182634,3.200055890763463,3.1866778740101154,3.167287589651597,3.1578513344132437,3.1516745251098115,3.1331014661707357,3.1075620552856513,3.0975973364825338,3.067867868316843,3.0563949380342637,3.018909050799998,3.000946311791016,2.9676845409244645,2.941368167549781,2.925716455004764,2.880449346644606,2.8679982209018906,2.8273486691626717,2.818308694315207,2.8022676156781925,2.7575695966509564,2.7313549344121,2.700418731775705,2.6641270623694115,2.649660447612246,2.645759413443341,2.6368506904319213,2.592690696488419,2.571494712008863,2.5415499173507827,2.522776633382496,2.4998317897138556,2.4911433819591373,2.4714337651856493,2.434425882877729,2.4130222109582293,2.3709306110826116,2.306016839939378,2.3058196881982482,2.3056211969935605,2.2194020790986455,2.140599914693106,2.1316178506189605,2.1172354197413217,2.031985664213048,1.975182989446835,1.9323340946252205,1.866567251109669,1.8351369344782213,1.8097660642005629,1.745030700920104,1.6686020006251043,1.6569193626335856,1.6443491389542917,1.5675869817949453,1.5033110042003592,1.4789322137080196,1.4755914425659737,1.467396787066778,1.3574643508384998,1.3135152884617485,1.2450928495717477,1.2201843446281329,1.1480983632154764,1.0801119490091953,1.0425154559798964,0.9826814379692053,0.951714643485138,0.8970594781595986,0.8514960378527485,0.8172645127229332,0.7738975728222313,0.743612945093238,0.716767689373178,0.6916837748993734,0.6718606387998713,0.667572120946458,0.651847587476662,0.632891117543954,0.6279738950225395,0.624023668430552,0.6093403144909537,0.6027762452751366,0.6004709246506588,0.5998927891363435,0.5994089896753145,0.6079228372015963,0.6265723822740377,0.6296266931855046,0.6367508838147895,0.651847587476662,0.6903689417299432,0.7089622964123015,0.7597317146773035,0.8172645127229332,0.8411410630204763,0.8714482185316035,0.9410864868824307,0.9826814379692053,1.0597397044662493,1.0755322467261657,1.1480983632154764,1.2020621770486848,1.2607197748799415,1.3135152884617485,1.37683086381454,1.4118798542249316,1.4789322137080196,1.5508675953121633,1.5731144943322954,1.6443491389542917,1.6943899593199951,1.806505013521031,1.8097660642005629,1.8107084922510248,1.811712148276242,1.896045908429783,1.975182989446835,1.9802730675996205,1.9840121874783518,2.027619016692382,2.054381439024427,2.117122372691844,2.128368524352033,2.140599914693106,2.2073127597967845,2.268138495435606,2.2881193936379063,2.306016839939378,2.381916174250053,2.4328071009447996,2.4714337651856493,2.476227213595531,2.4844477275709,2.581814712335433,2.6368506904319213,2.697251782149708,2.762139434495685,2.8022676156781925,2.823064143124607,2.965695893840908,2.9676845409244645,2.9693533978873674,3.1213007217614477,3.1331014661707357,3.1504937484776248,3.254641003841776,3.298518391417007,3.3765117099026227,3.3926392056784103,3.463935316663278,3.4948089942217475,3.3454196001911845,3.4615664069844208,3.463284003378247,3.463935316663278,3.4655606233883933,3.5810862418595253,3.629352241909551,3.700952430971313,3.735885665516655,3.794769167155822,3.8276717718227378,3.9558095818208656,3.9601860924020933,3.9634731172016444,3.998277796824823,4.11398967830273,4.1256030176483645,4.1393872718559575,4.272580355028497,4.291019942894637,4.31179525303301,4.428701868915093,4.456436868140909,4.492022053825538,4.573489669942877,4.62185379338718,4.701375373544977,4.706357459611402,4.787270718633451,4.832099007479332,4.949801515345992,4.95182593291846,4.952687643879724,4.954780485632337,5.067991294434032,5.118104569125995,5.187099070174694,5.230164564317338,5.283521494372266,5.308597661205797,5.385736640347368,5.432423563106861,5.448938419618537,5.482121776827627,5.556041215136778,5.61435534486481,5.678967194460498,5.734717369443949,5.779772270111081,5.800215945616204,5.848210610182933,5.912209229575703,5.945189195357353,6.012742695542634,6.108037211759033,6.109331673417973,6.110606120603624,6.1823606845189865,6.23885731830233,6.250918125255987,6.276023045849895,6.304285736313474,6.317644888609491,6.329881145592628,6.3381646893250405,6.348581167970757,6.338176076844617,6.329909810022251,6.326524925555933,6.309631235372963,6.276023045849895,6.25055904069818,6.2341371511607555,6.171514186913116,6.110606120603624,6.083209940122172,6.041215330015321,5.9818997012944735,5.945189195357353,5.873295337592408,5.832159174678315,5.779772270111081,5.757821211888164,5.687521012595884,5.632182299816861,5.61435534486481,5.589610210716463,5.488995651089944,5.448938419618537,5.402785050281405,5.334696150198543,5.283521494372266,5.226562516582435,5.179784293697786,5.118104569125995,5.045386122512269,5.01506918513285,4.952687643879724,4.927867017412169,4.896986790535543,4.853785418117727,4.793768862761775,4.7889849327320295,4.788676870186155,4.787270718633451,4.76995408099112,4.769122539897587,4.769383163001857,4.771299982729346,4.774028306442453,4.775215384821646,4.787270718633451,4.790594160707952,4.790740742144365,4.790770836237508,4.812210602581143,4.81611421838776,4.8183925800728264,4.834062285041934,4.8424414934446,4.8504647664197655,4.856843569384225,4.870435947441605,4.882636507204065,4.887975311755206,4.9016215961597,4.910644469965712,4.9328682394110235,4.937342847864658,4.940396875156191,4.952687643879724,4.976036163513623,4.98282393027533,4.997232563014906,5.015837639513515,5.036192275291764,5.058003510863326,5.083759463098762,5.095817648841345,5.10211525590036,5.118104569125995,5.149798058478122,5.162819872176515,5.191276226198939,5.196773357768507,5.22862643725092,5.243061985598853,5.283521494372266,5.286434931651943,5.287416748210976,5.288680548484862,5.322404735459884,5.3332085228093185,5.3448857549982325,5.352275992174066,5.366670848662599,5.376777353270898,5.380212952720031,5.38986069675259,5.395280493304657,5.401808441104542,5.405614282688422,5.408731964499712,5.415877400917401,5.417165644155142,5.419232327335351,5.4271586261129166,5.4275407725051945,5.4289471031799525,5.438438748493374,5.438532141439303,5.439165713900659,5.448938419618537,5.449690203817319,5.449742844818049,5.449818004272538,5.45758673609093,5.458017725070006,5.45850621789139,5.460379397620532,5.460527803428844,5.4602775355326685,5.455776631058841,5.455776631058841,5.4553310649198465,5.448938419618537,5.443106238284445,5.442552937094604,5.4407058255417,5.421543805734652,5.417499293235295,5.406080653320583,5.3925829947661015,5.381093215635978,5.356756189089934,5.3473257458959065,5.32964955385688,5.315690459120647,5.283521494372266,5.233576463705067,5.153315029475744,5.118104569125995,5.0627285686888435,5.02643662349727,4.996066313648704,4.952687643879724,4.935220063625069,4.9280596980492835,4.89036142949754,4.875881994735362,4.83357270141847,4.812001099489553,4.787270718633451,4.7363591895789146,4.694160489107263,4.6557254350163735,4.62185379338718,4.567054662763427,4.50302067643954,4.476824233468909,4.456436868140909,4.387117970217128,4.306824324534848,4.298659852136712,4.291019942894637,4.2188867899046,4.152599713164795,4.140489266731448,4.1256030176483645,4.06785094123491,4.02306994932305,3.996010958206078,3.9601860924020933,3.9243744823388678,3.896705176252473,3.851820215009093,3.794769167155822,3.7794295056615095,3.767957614907557,3.7115250096397663,3.7091760999559007,3.6514760577057856,3.643029327341882,3.629352241909551,3.5843144117215413,3.5603254597491887,3.5337340354810536,3.5178437337021773,3.4936872384579853,3.4867641062072057,3.463935316663278,3.448591583883596,3.4440612286913623,3.4389579702272606,3.4158282354279716,3.403777180163953,3.3881969779964756,3.3855187530809,3.3668704876285442,3.3534718118835904,3.3355734557447514,3.3258546277180425,3.3193298944666774,3.298518391417007,3.278118522142152,3.2709216650670543,3.250106652475811,3.229039509067701,3.198241372952377,3.176042218274196,3.1331014661707357,3.118844246526894,3.1107642124368997,3.07945653143953,3.0575851955673166,3.012029853618259,2.9957749857146343,2.9676845409244645,2.9345343733710623,2.91478093081866,2.8764943421300755,2.8584233627536193,2.828191367666866,2.8200873061433427,2.8022676156781925,2.7678073568565953,2.7517499471605973,2.718850283132265,2.717900319133114,2.6847526944393874,2.671397527955503,2.6368506904319213,2.6242036079486395,2.6186610037743483,2.6018673689562384,2.571779408806581,2.5418254221033614,2.5170800257626684,2.4714337651856493,2.456507972137315,2.44571655276978,2.3831990323296584,2.3360805269291527,2.3118979989263515,2.309187186542201,2.306016839939378,2.2242502071258006,2.1934119842955484,2.140599914693106,2.138716219333303,2.136459024559704,2.0574746706237566,2.037567832948964,1.9773199814890958,1.97642729094244,1.975182989446835,1.9076781213384848,1.8596770011005566,1.8431074048819198,1.8097660642005629,1.7849932091114544,1.7697322240226336,1.733840285222116,1.7295229416514628,1.6920622754850134,1.680855714735359,1.6443491389542917,1.64024450338177,1.6373799811491008,1.6333305297175622,1.610663917371495,1.6043387555236048,1.6201236210273535,1.6443491389542917,1.6693663763930582,1.6772892315728498,1.7401066375669565,1.8097660642005629,1.8164477728278863,1.820221954468594,1.8730519858071242,1.890500759744973,1.9563402235076355,1.9657082589477959,1.975182989446835,2.032823588676898,2.0702726173293744,2.099953328348823,2.140599914693106,2.1657464484531275,2.180131114905322,2.231857816353747,2.271286126801466,2.2935458995982607,2.2990831188403247,2.306016839939378,2.3738267017737495,2.429908246991113,2.451012675277889,2.4714337651856493,2.543134246423527,2.630035140541839,2.6368506904319213,2.6377658951905367,2.6396063355302415,2.7493675858899946,2.8022676156781925,2.876038019122209,2.8978282081943547,2.9676845409244645,3.0219135600253217,3.0767155475211023,3.1331014661707357,3.212365552388503,3.217940003226138,3.298518391417007,3.3454196001911845,3.337396214634275,3.430542292323695,3.454108126580447,3.463935316663278,3.4918146639452186,3.5671068872593246,3.629352241909551,3.6815326137627657,3.789165045188456,3.794769167155822,3.797457328389596,3.806498474622215,3.9204153951269873,3.9601860924020933,4.034089209816189,4.0488964265885325,4.1256030176483645,4.190092221187282,4.232980446723847,4.291019942894637,4.338036329821206,4.419670556057456,4.456436868140909,4.483788595721887,4.612197797469374,4.619733575080549,4.62185379338718,4.626417914489041,4.735766444161978,4.787270718633451,4.849663509926472,4.926526213840825,4.952687643879724,4.9617954191082525,4.982606939542018,5.07060103910637,5.118104569125995,5.183755689028683,5.2411336525376235,5.283521494372266,5.300576440238286,5.346530557692322,5.412836925196871,5.448938419618537,5.520627266113072,5.5674851727564985,5.61435534486481,5.6277818100049135,5.651460152849994,5.708767349193508,5.779772270111081,5.782404581840092,5.784226591603199,5.7834961556895355,5.779772270111081,5.7481687292733135,5.739179140380443,5.666094889779483,5.61435534486481,5.5680351062170494,5.49821171671949,5.463879946493144,5.448938419618537,5.416796524215362,5.343102728088812,5.283521494372266,5.215982886338304,5.176137369423097,5.118104569125995,5.082947387539981,4.962897904112317,4.952687643879724,4.946339783586003,4.923614619804697,4.816529283593461,4.787270718633451,4.711384298496657,4.667527550288396,4.62185379338718,4.614192159209271,4.608976787211239,4.604591073407228,4.564380226667431,4.538894513068598,4.535058608335152,4.534639377131471,4.515547786714938,4.515547786714938,4.51971417087541,4.520476177890702,4.524700663421836,4.5293323975174555,4.543251033352668,4.5541741081439575,4.5599588249561585,4.575885600757493,4.583944556238366,4.608134275296392,4.612048882343368,4.613871141532426,4.62185379338718,4.6449298633537435,4.650287642921265,4.65574830062207,4.6737335755957385,4.685449312263534,4.6990325295143105,4.700982075959677,4.717915758125052,4.728971306346393,4.740395242062245,4.749936156116975,4.756221186447199,4.782442424129298,4.78338803467304,4.784071591435964,4.787270718633451,4.815699658372569,4.822501779266597,4.836094577059944,4.849757527441474,4.8655367404127094,4.886079282704845,4.9004386069469845,4.914482571293792,4.924182850726503,4.952687643879724,4.967232090488588,4.972711741602387,4.986617237057729,5.01407605237379,5.038122826353153,5.060943709384402,5.0948994025991166,5.103770312183553,5.107507307141923,5.118104569125995,5.147916944360171,5.157276846245924,5.168759221179249,5.180893279852738,5.195552307709168,5.207073951443967,5.209296056553702,5.219940970096868,5.224949678881707,5.229463735065702,5.232627692452603,5.234231010305573,5.237096793318175,5.237096793318175,5.235535451964623,5.236899529353549,5.236899529353549,5.233267945799479,5.233934880364373,5.233934880364373,5.227094930678671,5.226904669159309,5.226698992706288,5.213338040550161,5.212284795323361,5.209158136784753,5.188156089688306,5.177317168310548,5.169751319748576,5.153762456780825,5.118104569125995,5.072853887569893,4.98866317261426,4.952687643879724,4.926250529338352,4.851131174342081,4.787270718633451,4.74447408171218,4.676501631507396,4.6413675232810405,4.62185379338718,4.544178570121284,4.505632654534082,4.456436868140909,4.450275748414761,4.443706237590655,4.368603065374334,4.291019942894637,4.287550648010715,4.284698206606086,4.261104987661746,4.214624299207953,4.154547445610243,4.141356327816533,4.1256030176483645,4.067222287694971,4.020191472607447,3.9921268707083044,3.9601860924020933,3.9164975739827614,3.880777998194956,3.84307181131933,3.794769167155822,3.7728101918161627,3.7583203770571156,3.7190964223861744,3.714012545230416,3.66833198103234,3.656905732567882,3.629352241909551,3.6103196434569664,3.6034050578161594,3.594773732088452,3.5727468063822556,3.5559504481511546,3.538656793613365,3.5338464363605215,3.515549373487765,3.5051824409166237,3.477344083978144,3.4738259697385523,3.47152562883225,3.463935316663278,3.431852024120527,3.4216299944626023,3.3933846221189174,3.3865251264094525,3.356106150840837,3.3373169379864276,3.298518391417007,3.282549175966154,3.2741969273160345,3.2419180339937945,3.222972396219342,3.1799533873059547,3.162829809105225,3.1331014661707357,3.101879702854304,3.083436915952123,3.043207545966551,3.0268268908665172,2.995213887744864,2.9865051118105175,2.9676845409244645,2.9341775947113593,2.9186739435692326,2.886199988197119,2.885516644792756,2.8536948021891053,2.840028346677549,2.8022676156781925,2.7959342586069864,2.7935732456188553,2.7877767489250385,2.751019005725434,2.7321202149601644,2.7027828575310293,2.67588438845502,2.660035115239494,2.6520867217866675,2.6368506904319213,2.5915904948933592,2.564535361682192,2.5262143579289233,2.4714337651856493,2.45653101022765,2.44378445342071,2.3807831035346103,2.306016839939378,2.3050822024996114,2.3041979194043636,2.2983932226194685,2.2321559055400675,2.1738667147785184,2.1618832708944895,2.140599914693106,2.1022600578806667,2.0806410385444742,2.0547856894258345,2.051797613691556,2.0229496085840584,2.0171609014498557,2.0041306494833204,1.9990347320896351,2.000084217126412,2.0061677320374853,2.0078886715071285,2.019365819170643,2.0348195974479477,2.049781423885112,2.0778731604106637,2.110286649554924,2.1232838136025247,2.1296963219526583,2.140599914693106,2.1820882512068396,2.200305781617315,2.2375967982468277,2.2718304269231497,2.2893488736893293,2.295721759127434,2.306016839939378,2.356016444295525,2.3842674428292385,2.420972797967286,2.4714337651856493,2.492199784380592,2.509575143594448,2.5745521093140864,2.6368506904319213,2.663468663969147,2.705718291108158,2.7672539127675417,2.8022676156781925,2.873827997292148,2.8910876501158835,2.9676845409244645,3.0344150633584857,3.065713085544269,3.1331014661707357,3.2096925675093466,3.2262573391429186,3.298518391417007,3.337396214634275,3.3392588234437337,3.4292904789708025,3.45269335534136,3.463935316663278,3.50432745105649,3.5590094026917853,3.629352241909551,3.6658881918385138,3.7326000780414095,3.7695643642242143,3.794769167155822,3.8696826687614863,3.9132588222743614,3.9601860924020933,3.9738025850837317,4.00185708940392,4.069583877962463,4.1256030176483645,4.164173930496894,4.224918006717132,4.249262711088866,4.291019942894637,4.315894401964945,4.338674660184708,4.338674660184708,4.345879934213391,4.344220261372568,4.33404061580228,4.309436779349687,4.301500121759982,4.299416880247087,4.291019942894637,4.27885206388199,4.278381310608708,4.278381310608708,4.26840866434852,4.268187425801511,4.268187425801511,4.264745217762735,4.265975173234995,4.266635989937125,4.269885291354582,4.271920400049995,4.273588009926188,4.287398407606917,4.287890171527112,4.288363646051749,4.291019942894637,4.31362359156892,4.317702683827095,4.323905451992376,4.344102034982468,4.357595880157545,4.378228687119648,4.381454143943296,4.4046333850197374,4.416663867265786,4.453901604559334,4.454744734276511,4.45514131561106,4.456436868140909,4.491520954111547,4.5013834864445545,4.514366660796632,4.524497823810968,4.541987133976532,4.556024036350104,4.565172971817864,4.577973617410974,4.585379276137267,4.60893663878541,4.611479032926763,4.61317401818933,4.62185379338718,4.640243759812835,4.643845393088554,4.649821177545574,4.667263312669208,4.675868688414198,4.691495254332386,4.695547315365465,4.70907015880168,4.724094095946402,4.736282206836401,4.745426010371121,4.7539816980943765,4.787270718633451,4.787856711188139,4.788026801876676,4.788469557067064,4.82730027930131,4.839816546300407,4.8710162017099865,4.872298291482336,4.898144381730399,4.91257586816276,4.952687643879724,4.956164150223493,4.957333078737044,4.959062179540396,4.989767366235119,4.9991025162721545,5.0085837781844535,5.015187334453083,5.023964675269049,5.029297062966522,5.029561753760591,5.031266873469406,5.025475859681343,5.023760913850836,5.022973732355647,5.013150117487864,5.004518958181661,5.000791333441402,4.991313545620036,4.9626458136472795,4.961404126789725,4.959066457314201,4.952687643879724,4.87581279178608,4.801794567433584,4.787270718633451,4.7857598375063315,4.6564820983448865,4.62185379338718,4.550436386330913,4.473333821859782,4.456436868140909,4.454413566477209,4.452554694578138,4.373056342807644,4.330954794892243,4.292459872062967,4.291698947999059,4.291019942894637,4.211595463424409,4.137124545196363,4.131109309629579,4.1256030176483645,4.0510614054562915,3.981889887990894,3.9714138872156166,3.9601860924020933,3.9008496375869495,3.858337543589453,3.834755770214217,3.794769167155822,3.776574156076766,3.7681784215820606,3.7549309021490433,3.731734382473592,3.7083557924823083,3.690700644331736,3.6734387107156863,3.659753977734754,3.6530384308134956,3.629352241909551,3.6172583525425903,3.6140852283176077,3.6074463763959557,3.579838026049945,3.5652949226622823,3.537695322282085,3.5269946433750334,3.5052166583668853,3.4924154182764724,3.463935316663278,3.4405253613315505,3.429600794954169,3.388610133293813,3.3835645133160437,3.3418483220486435,3.3262616314840567,3.298518391417007,3.2665397077245117,3.2483801496774936,3.2082832833473747,3.1910796168692572,3.1612016747210605,3.152418409379928,3.1331014661707357,3.1009669826092514,3.0865210272293817,3.0568006990211716,3.0534327757033086,3.0250317214888165,3.0106774832172825,2.9708652038993577,2.969974681519087,2.9694249905150976,2.9676845409244645,2.930232169287038,2.9186122519791695,2.8866851712690975,2.8858122806258777,2.8577347800821737,2.8397571106945607,2.8022676156781925,2.785957153349421,2.778001376964336,2.738036897741009,2.724143422304712,2.6770782976089382,2.660204981403009,2.6368506904319213,2.5896263056502677,2.5539518261986016,2.518590161575732,2.4714337651856493,2.447180246806359,2.428279246458075,2.3818834010141288,2.360340944376274,2.3248991510520867,2.319288590735054,2.306016839939378,2.269971296498184,2.254632468140752,2.2449872984887547,2.236971190552106,2.2213104600500637,2.2213104600500637,2.221440278803481,2.222050630818811,2.2343157976229104,2.2388587725511107,2.252154203744694,2.265616051065745,2.306016839939378,2.3068229995698957,2.307042420838515,2.3077091765018745,2.352436506207356,2.370135914512037,2.404247132953917,2.436262971090544,2.4529245568711424,2.4599621685406143,2.4714337651856493,2.5255019491432353,2.5615137946720656,2.5964134974656083,2.6368506904319213,2.680109925545465,2.7337810572204466,2.774486828624336,2.8022676156781925,2.8690956985966967,2.8925067709505345,2.9676845409244645,3.0311111331787695,3.069532421961749,3.1331014661707357,3.213831244965446,3.219276330999815,3.298518391417007,3.3392588234437337,3.342601918513191,3.429021689453217,3.4511780450681915,3.463935316663278,3.535803299611347,3.5486242169077187,3.629352241909551,3.6460926015261865,3.669137653542908,3.7320416677842037,3.794769167155822,3.814957006690708,3.8353854121573203,3.88063313955195,3.8889572152053518,3.935348280575104,3.9413868214218315,3.9601860924020933,3.983447231862346,3.991793331235341,3.994659100214893,4.011744611901161,4.022841157492026,4.026065084348167,4.0302303465152285,4.0401223874446455,4.0441578985124575,4.044289619541729,4.052331664038453,4.05664253308939,4.058475977346838,4.063307585064324,4.0682640915789,4.0730651020808395,4.076322771680408,4.082029580053108,4.093825511884395,4.096412703294735,4.101386943547391,4.1256030176483645,4.129437758939128,4.130192838326074,4.1318644176687584,4.164505452037359,4.175064978525006,4.2009821116460255,4.204693583452974,4.23150780538638,4.2481863974284,4.291019942894637,4.2941593078643585,4.295203338125463,4.297048843823818,4.334402638743697,4.348371896408132,4.371288006919391,4.3723726511778285,4.395616906449225,4.4079714890492205,4.431402653413874,4.4373568456932,4.440867673671844,4.456436868140909,4.469725498473931,4.4723410076125045,4.476200433918505,4.494758740274516,4.501384839109532,4.511820151450564,4.519015247030408,4.528503286679344,4.542821727466562,4.544448595638041,4.554408191958753,4.56445243905536,4.575187505608989,4.579949732680978,4.586129730050933,4.605786026807998,4.606951155827799,4.609173938039165,4.62185379338718,4.634360804749262,4.636664637902671,4.642945107334025,4.661893276099674,4.669168211759915,4.688409912913302,4.692564249946551,4.702999469298353,4.718722417301418,4.727151683389183,4.729891284929931,4.727965315532902,4.733802575531433,4.733802575531435,4.7019367123212135,4.6984663545901775,4.685287357431388,4.656734087467603,4.62185379338718,4.544364196880803,4.5351007078131715,4.456436868140909,4.4154126361804185,4.346131890440063,4.308774467458779,4.291019942894637,4.210946598036282,4.190776494542682,4.1256030176483645,4.119048872925015,4.112961006689636,4.041578038420694,4.022799524698776,3.9684296666142505,3.964797133819502,3.9601860924020933,3.908837670312483,3.8833883428484715,3.8578365100004035,3.831081356754332,3.8162778018469243,3.810462944139468,3.794769167155822,3.770979756486941,3.7642083759106537,3.7503041218453923,3.7331800094063627,3.7154136465529977,3.692452428325751,3.670018871641979,3.6572894732683476,3.648944395288318,3.629352241909551,3.6005895436058974,3.588948124781407,3.546598681798981,3.5465039327212082,3.5087938745547405,3.492995972450089,3.463935316663278,3.435213865941586,3.419987440570681,3.3780971998276037,3.371140078529576,3.3358357011248794,3.3244158739037655,3.298518391417007,3.274549123727316,3.264437931273233,3.2450443495110104,3.231236259054593,3.2104341509525254,3.1932528236260582,3.175214157780882,3.1664250363100592,3.1596735532051907,3.1331014661707357,3.126306997108447,3.124626414296025,3.119979928517922,3.0891346375409547,3.076615596990673,3.042192061389544,3.0281063648052937,3.0035161802797194,2.989566543612212,2.9676845409244645,2.927461486528024,2.904009263940348,2.860155804922644,2.8022676156781925,2.7892737810104657,2.7799560938881065,2.7171518295105095,2.6998698649404984,2.650352403271225,2.644516470723314,2.6368506904319213,2.576365074120808,2.5344078364929628,2.513104145542674,2.4714337651856493,2.4576335816569834,2.4509368222718892,2.4451961799896447,2.4194407397972286,2.404081640596763,2.4024778918278473,2.3999715683701783,2.392806945042741,2.39930204476621,2.4013952968146555,2.4110517762232355,2.423425931535995,2.447526220499074,2.454033397968784,2.458951303788327,2.4714337651856493,2.5051712663568093,2.5181773423940115,2.560497573905198,2.576303446255488,2.6079038904176697,2.6198652016570216,2.6368506904319213,2.697558321649696,2.755501655106541,2.7810199841780374,2.8022676156781925,2.866634944944188,2.8920236604223906,2.9676845409244645,3.0227312348790862,3.0791341796891682,3.1331014661707357,3.2059349559117365,3.221353004961893,3.298518391417007,3.342601918513191,3.3405618192622404,3.4110806069949327,3.441848420071741,3.463935316663278,3.530387869343988,3.602753975685461,3.6145975068668594,3.629352241909551,3.6842024253848624,3.723057185123734,3.74475855590177,3.794769167155822,3.794815589995599,3.7948350238429605,3.7948507537342895,3.8296280705980212,3.8389193968703506,3.8453600536444483,3.8541812390300016,3.8636388709162777,3.8705003891706653,3.87144958274466,3.8770461185329133,3.882215183227048,3.882906610352114,3.882906610352114,3.883600095244704,3.884445696814394,3.884445696814394,3.885967940517567,3.8876837691609616,3.8876837691609616,3.8967507151131944,3.904455459210851,3.904455459210851,3.9176551414177148,3.9538165764730433,3.954607690541387,3.9565276815735153,3.9601860924020933,4.000812966225874,4.015271020259997,4.0522098350786155,4.071087979240913,4.095322529944728,4.105864548372155,4.1256030176483645,4.155021237507997,4.165934255695138,4.188899831129008,4.198406630244474,4.222015496904479,4.238469851505354,4.26596542736106,4.272280224208949,4.276179371607599,4.291019942894637,4.306132933224195,4.309024888491569,4.313560929683263,4.329444018027516,4.3352868336600565,4.344951145051667,4.350945927722407,4.357913442831791,4.370077678658525,4.37058330442799,4.376503007839911,4.385235834579772,4.388453227533189,4.389660323439328,4.39196278819278,4.395644839911082,4.395644839911082,4.389404773282523,4.391166066938904,4.391166066938904,4.3697594653339635,4.3667956700110615,4.365033917166484,4.339507259293901,4.291019942894637,4.266190908409444,4.179134803661084,4.1256030176483645,4.0872797896955415,4.061477764918839,4.021365628510777,3.9601860924020933,3.957335076982563,3.9563284246297705,3.954035883431617,3.9162476025228976,3.901850780078494,3.8711760626122302,3.8627225490937764,3.840818893052923,3.8265320287391766,3.794769167155822,3.778409621890635,3.7726760640509998,3.7516046834742145,3.729284179755579,3.7035360124950145,3.677674408299392,3.629352241909551,3.620650934443134,3.616468818440806,3.602351208935067,3.567703614896681,3.5398795600138904,3.516789186231172,3.470467093036726,3.468177765467855,3.467208801188015,3.463935316663278,3.4334712592668843,3.425777218080503,3.414942398250785,3.4077583573512626,3.4010596461295606,3.388287222398331,3.387780518357534,3.3849460941316565,3.369619906313238,3.363241090798166,3.3590979615634797,3.3416579562076727,3.298518391417007,3.294404586618005,3.2929270269512774,3.280671788401727,3.230068395047515,3.186289479153726,3.159473102395965,3.1331014661707357,3.0814039735342993,3.037885371521188,3.0017240734965096,2.9676845409244645,2.9212386164043203,2.880451014310254,2.842836162475227,2.8022676156781925,2.766929443621959,2.739637161130444,2.699341428616318,2.6368506904319213,2.634697307340052,2.633496614858509,2.6319731443250696,2.589399500137519,2.571535830089374,2.5639263821587432,2.5610106426281494,2.547731621046843,2.5500217905456095,2.5506438473232764,2.5571111458042983,2.5718359687905687,2.5821973817537804,2.5954124120147863,2.607234813024008,2.6368506904319213,2.6568831309931156,2.6665346236946705,2.7238337600346876,2.747011857137255,2.7861454895206945,2.7940419485981396,2.8022676156781925,2.838229077137952,2.8977262363420646,2.9676845409244645,3.0203342235555546,3.083872577844251,3.1331014661707357,3.199519867124933,3.224162328812434,3.298518391417007,3.3405618192622404,3.324696348343946,3.360768649479626,3.4139861907530147,3.463935316663278,3.494721761991366,3.5197960337258802,3.559094396122047,3.590702730555652,3.612431532182301,3.616871532356715,3.629352241909551,3.65649619016777,3.6646187689113674,3.671732018903917,3.681639400007862,3.6889613628943234,3.6930143451551505,3.692412024400184,3.692412024400184,3.684055148025177,3.673955513823225,3.673856155768398,3.6641866481079894,3.629352241909551,3.6270223552130645,3.6250567406342036,3.5280880513852324,3.463935316663278,3.3903549310409318,3.37723739923441,3.298518391417007,3.2650919888531487,3.2152878519637396,3.162367254167992,3.1331014661707357,3.0669345183102594,2.9855575778398507,2.975655905077055,2.9676845409244645,2.8978120088927515,2.8376539068285123,2.823452316442694,2.8022676156781925,2.7653753734937645,2.7474051491533107,2.732687033449875,2.7272891483875714,2.7078851997845,2.7078851997844993,2.7086099248932216,2.7103428940017107,2.7289315621616126,2.73529608903739,2.752654593320816,2.7691637446338655,2.8022676156781925,2.8323313510195725,2.857528682291268,2.9195876243682966,2.9676845409244645,3.0395622861484384,3.0640001640973127,3.1331014661707357,3.2114329177589944,3.225337770657604,3.298518391417007,3.324696348343946,3.1564277941491525,3.2093419550518787,3.2631189380716066,3.298518391417007,3.3435654973007196,3.3764713130739565,3.403213677999217,3.4378218143814614,3.4463587945357244,3.4441942612120098,3.4580649682811107,3.4580649682811107,3.4256220349050768,3.3879439711973003,3.3319260094443504,3.309135046858059,3.298518391417007,3.2864842912482235,3.2454366449145367,3.1596972157488326,3.1331014661707357,3.0639680130598874,2.9861750991201257,2.9783667300633745,2.9676845409244645,2.929175924098266,2.914582101965731,2.9139657745313503,2.9137287167454833,2.9135072042575167,2.929383137178525,2.9676845409244645,2.9887494342493373,3.0212648121839134,3.1072584914704446,3.1331014661707357,3.1564277941491525],\n",
       "\"y\":[1.323889937417435,1.3238253501699337,1.3237159837774626,1.2698462080951098,1.2548840565494523,1.233105318503609,1.2120811911273104,1.185942762928971,1.1529279760828834,1.1495723002655702,1.1170014693084895,1.093872466264108,1.06727667902183,1.0480601756880072,1.0340044330653115,0.9868297338801102,0.9791188820675258,0.9728064931170537,0.9120146668325817,0.9101775884470444,0.9079847977453839,0.8464844465825245,0.841236294826563,0.8321136388636279,0.7920675369581827,0.7722950012060816,0.7458857296140757,0.706034126254766,0.7057207150791887,0.7033537075855993,0.6985683667620033,0.6980468850753936,0.7004745786077824,0.7033537075855993,0.7321739800454332,0.756728292242173,0.7664826032056449,0.7722950012060816,0.7894661258624969,0.8126287250430724,0.841236294826563,0.861171622855815,0.9035915262170922,0.9101775884470444,0.9140202714679657,0.9396914972731012,0.9747509724661385,0.9791188820675258,0.9841650817609042,1.0431499086273006,1.0480601756880072,1.0525222325555137,1.0969432470501403,1.1146901384174037,1.1170014693084895,1.1205806580623432,1.1709035790421418,1.185942762928971,1.214784207659401,1.2233275892312148,1.2548840565494523,1.273439871503966,1.3125642678684977,1.3177943388958027,1.3238253501699337,1.3480326390611252,1.3664900452658464,1.3502175482902552,1.3242372293076925,1.3240431318454013,1.323889937417435,2.5660723565753103,2.5647686353386026,2.550383120606836,2.528796679077647,2.495827341718121,2.4912213943515797,2.484108609077071,2.445618363290825,2.426886048097639,2.3972135784767112,2.3816131508743568,2.3579447544771575,2.3491032791583497,2.3290680391079976,2.3017385763507288,2.289003460856676,2.2568652385952865,2.246160216060891,2.2200621672361947,2.213689852269074,2.2049641962404993,2.174534345616189,2.1511208736157132,2.1367088241545438,2.120854372346909,2.1002600308296,2.082179579995231,2.0646617560970113,2.0470955706525387,2.0300975069249136,2.0132382863747496,1.9972045339901352,1.9839027409917045,1.9675286168872446,1.9442969927542681,1.9399228227156402,1.9376380911947755,1.934283963424686,1.9224958900011262,1.9155739226509616,1.9105177517200054,1.9103375253312795,1.9052481625453423,1.903572521489076,1.9027828682406125,1.900998482299212,1.8996202628711045,1.8983910388599692,1.8972427540368586,1.8951359995700554,1.8916337083042571,1.8904090130025604,1.8881234109835607,1.8786588522707244,1.878261765010302,1.8776758069213941,1.8753556991337867,1.8662457026662476,1.8645283191614426,1.859432766280864,1.852372053350241,1.84696894148242,1.8364098308851395,1.8315473496315104,1.8249625476868334,1.8200237796732819,1.8064144055133053,1.8024399284855481,1.8012998142015362,1.798583093479198,1.787231155424267,1.7820371644088504,1.771645201977155,1.7713842622274032,1.7636878777020288,1.7587557673617824,1.7507995031578196,1.748734633830772,1.7472757789496902,1.7386497452107945,1.73856341347553,1.7384810112413303,1.737473111892823,1.734031058663167,1.7338039308045707,1.733198294656448,1.7305492851499484,1.7302316467496115,1.7288711173486342,1.7250840000425813,1.7241055050124472,1.7201260283618258,1.7151808343010875,1.7114186374304388,1.7009051343818098,1.6988877069998654,1.6906682769619876,1.6848480921906135,1.6685318182723416,1.6668897245380143,1.6663753244182007,1.6656890515098675,1.655335989581571,1.6527535649347436,1.6539133695979982,1.657334913693362,1.6575171280594225,1.6609076980388982,1.6685318182723416,1.684568855569482,1.6937095782660063,1.7144984358850741,1.737473111892823,1.7474519235098902,1.7568481781438314,1.7802282040908568,1.8064144055133053,1.812485571592601,1.8174971777454583,1.8298603244731022,1.8380220974856418,1.8565978968553192,1.8599001612182362,1.8702336596271985,1.871521486541797,1.8707707175881292,1.8643457241131158,1.8630196908449634,1.846028889535059,1.8425569574796428,1.825849312679646,1.8164133580185502,1.8064144055133053,1.7816383818827322,1.7555954822829238,1.7455115374925483,1.737473111892823,1.7060714065909788,1.6828731445126928,1.6685318182723416,1.6666002057860436,1.6639399763450018,1.6300569135432919,1.5995905246518602,1.5939147193801495,1.5879543825881695,1.5637273721040716,1.5561043343994378,1.5378387316189364,1.5352047908110582,1.5306492310313788,1.5095147509567641,1.4968871215567936,1.482116981695444,1.4617079374108974,1.4521741560910102,1.4437563566767442,1.4172494185462337,1.3927666437904151,1.3798600082930261,1.3612240494857564,1.339828929682572,1.3238253501699337,1.2983882110950877,1.2567234819007846,1.255804970997541,1.2548840565494523,1.2348007543624617,1.219719355718349,1.185942762928971,1.183222937088646,1.1790603201924852,1.1734193071790302,1.1589946378872145,1.1458042212034738,1.1390592584367503,1.1281240775737467,1.1244696533054541,1.1212840668793462,1.1170014693084895,1.0948347065629123,1.0789707777852695,1.0480601756880072,1.0187138478607705,1.0096172254262048,0.9791188820675258,0.9636675741015464,0.9511870691434354,0.947099041929532,0.9461887521036112,0.9386784708315212,0.9275658090367043,0.9101775884470444,0.9024863803472019,0.8989344303565399,0.8624315718575519,0.841236294826563,0.8201952137690207,0.7894459217213936,0.7772068313783884,0.7722950012060816,0.7563797601608058,0.7318323095156969,0.7033537075855993,0.687984712290818,0.6655282026309624,0.6481777614702469,0.6344124139651179,0.6128747299459776,0.5924553429027095,0.5842675133971515,0.5654711203446365,0.5634792840884901,0.5626862964896797,0.5626715749089377,0.5564607754482638,0.555481253819146,0.5561479295838079,0.5600213589022967,0.5605019765679686,0.5611289282646923,0.5654711203446365,0.5692372469489864,0.5696983637197444,0.5709875157518485,0.5778610221048504,0.5795297215146813,0.5835456559917582,0.5864712777054035,0.5885283754367987,0.5900881108965996,0.5897377596136031,0.5897377596136031,0.5850124080843071,0.5754893555125613,0.5729482875834413,0.5702065346107488,0.5654711203446365,0.5438180504367023,0.5301782411208769,0.5149764913137376,0.49652982672415513,0.4837545160519734,0.4731116988587192,0.45222045523674614,0.42758853310367373,0.4207733589910654,0.4152778973505087,0.39652356602822936,0.39376590091618047,0.37075689121925803,0.36782946049505627,0.35864723948319144,0.3509388849075976,0.3483832001977363,0.3483832001977363,0.34761611817458116,0.3477594423037682,0.3496995548105599,0.35864723948319144,0.361432407571304,0.36191898652264376,0.36246629216247994,0.37172521051466356,0.37405184255701274,0.37405184255701274,0.37490001379510973,0.3744313628114022,0.37170898596588886,0.3604349728326315,0.35992188272588743,0.35953245566446634,0.35864723948319144,0.3366309332716111,0.3256215180822841,0.31154704410693723,0.28970594586271003,0.2841778420556964,0.28019794009361076,0.2542318769140022,0.24728497337900412,0.2255489788105396,0.2234762287786798,0.22076465224222863,0.1908585972268555,0.16357149696155426,0.15783877325935292,0.15182335862174723,0.12369455749386793,0.11570443374548267,0.08288206500126538,0.06764437274663448,0.02466342911911834,0.013940771380783978,0.005298716645615986,-0.03891472658909567,-0.05500052223969787,-0.07717681998845372,-0.09631993439734465,-0.12394181586017927,-0.1518789126167137,-0.16816715318463027,-0.19288310948066067,-0.20697841672604733,-0.25806911917015585,-0.2618244031011425,-0.264016576041155,-0.27531940104528374,-0.31838494822509933,-0.3307656967216239,-0.3505296746610571,-0.37359940517532886,-0.3997069903421058,-0.4294982929699258,-0.44115030697850477,-0.4686482839625872,-0.48550388171911996,-0.529488409535614,-0.5375895775830686,-0.5426127195487669,-0.5679045508141125,-0.5977623989297145,-0.6065308712035504,-0.6207772256465622,-0.6524086675710445,-0.6754721648240318,-0.7085178169434743,-0.712052778773463,-0.7444134584445137,-0.7646397168175718,-0.7994776112757997,-0.8133547520649951,-0.8223773748291432,-0.8758520430813408,-0.8810513418190418,-0.8822960456854769,-0.8841539268793692,-0.9377739358455601,-0.9512373393059583,-0.970849356036648,-0.9958030635010111,-1.0201786329264397,-1.0546208117527844,-1.054669854817329,-1.0891199265469216,-1.1144494585897493,-1.1357775988543537,-1.158061220167403,-1.1754580181050311,-1.214328799835048,-1.2270025137878848,-1.237555756289868,-1.2907912810596973,-1.2959438074083662,-1.3003991263376835,-1.3443685681058781,-1.3624557312046077,-1.3648851010288476,-1.3682455011703696,-1.4210861615956785,-1.4338263946493295,-1.4535787647057297,-1.4769321527213535,-1.5027676882698109,-1.5309267145775558,-1.5487512987902994,-1.5717089818902927,-1.583661369552393,-1.6259158437783636,-1.637337994115239,-1.6406502755107741,-1.645643656035269,-1.6947784205302967,-1.7095915691312555,-1.7279338884076543,-1.7586446308490364,-1.7785328627517374,-1.7970391952379403,-1.8336868872623016,-1.8474741563722188,-1.8571624089083503,-1.8907114808756982,-1.9107979207773973,-1.9164154499927004,-1.9300760759565623,-1.9598655238946145,-1.985356743613182,-2.0073376277729618,-2.0499232497918207,-2.052696901010929,-2.0542980372336634,-2.060957219591592,-2.0974778245474552,-2.1232393308541453,-2.1434956275814354,-2.186921088272628,-2.189995971313466,-2.1921806244746267,-2.2034355342513434,-2.235436817966666,-2.2611219180951085,-2.2825009119606983,-2.326896765582461,-2.326896765582461,-2.3133458026708804,-2.3180898244420494,-2.3180898244420494,-2.307874016588646,-2.3063483197512284,-2.3063483197512284,-2.3034586103032426,-2.303501422661345,-2.303501422661345,-2.303166353212535,-2.305721194084075,-2.306623083246182,-2.3075058766896612,-2.308370194269916,-2.3048913474802406,-2.3044879219429157,-2.303920831372076,-2.290943269912355,-2.2837790259701967,-2.277400376916836,-2.269865039206238,-2.2611219180951085,-2.2351298324039064,-2.2070523712051813,-2.1980074214207956,-2.1921806244746267,-2.171729438316814,-2.1544957420551425,-2.1232393308541453,-2.1118519316726365,-2.0924985304716337,-2.068606803588796,-2.0542980372336634,-2.025222091687835,-1.9992716476607577,-1.985356743613182,-1.9824844694106765,-1.9779398507144383,-1.9402992401172245,-1.9164154499927004,-1.8963804546123295,-1.8557022646521217,-1.8502287767156322,-1.8474741563722188,-1.8415417032514183,-1.801862096611487,-1.7785328627517374,-1.7501636914762955,-1.733952269053137,-1.7095915691312555,-1.6964827482659373,-1.6432426598667074,-1.6406502755107741,-1.6390477853655314,-1.6299247659962828,-1.5830090267578503,-1.5717089818902927,-1.5520596150562218,-1.5291432610258298,-1.5027676882698109,-1.4787682432077065,-1.4406188909549797,-1.4338263946493295,-1.4316328285989801,-1.4285092885357815,-1.3953586870901193,-1.3648851010288476,-1.360022334756235,-1.3557938514038068,-1.3280915640307716,-1.2991410222950321,-1.2964868528689286,-1.2962290992752012,-1.2959438074083662,-1.2632266324283639,-1.2331782956146657,-1.230011122865792,-1.2270025137878848,-1.1928688076798406,-1.1925083002120784,-1.158061220167403,-1.1554255451650448,-1.1517982565889064,-1.1145064130671858,-1.0891199265469216,-1.0717373029590256,-1.0377501518726309,-1.026306438339088,-1.0201786329264397,-1.005468594348562,-0.9787006638899176,-0.9512373393059583,-0.9297624694624624,-0.8914173837389963,-0.8822960456854769,-0.8782775002435614,-0.8645884941589213,-0.8269331843274315,-0.8133547520649951,-0.7894487614384618,-0.7736112912190372,-0.7444134584445137,-0.7196976358122487,-0.6948985978842592,-0.6754721648240318,-0.6642922966533433,-0.6082683493102161,-0.6069160692516458,-0.6065308712035504,-0.6059268233332022,-0.5524253943460504,-0.5375895775830686,-0.5147315026039831,-0.4961887528813578,-0.4686482839625872,-0.4396764025689821,-0.4261166551348494,-0.3997069903421058,-0.38367032242208676,-0.3361130299007149,-0.3307656967216239,-0.3278378112136471,-0.31785745943026056,-0.2779289917878729,-0.2618244031011425,-0.2286753363142311,-0.22428498021630316,-0.19288310948066067,-0.1821835964849634,-0.15986685045001137,-0.13740903961954842,-0.12394181586017927,-0.09285742147032972,-0.07860481664165953,-0.05500052223969787,-0.04925446507083109,-0.03836620070403729,-0.007636036342362651,0.013940771380783978,0.03360363408159728,0.06440640732011005,0.07323845601862145,0.08288206500126538,0.10472616810129365,0.12244893159280412,0.12986557308455904,0.14262982406898406,0.14545121626628887,0.14619072508888697,0.15182335862174723,0.1538243149387939,0.154041849201088,0.15446080090512604,0.1595820467354998,0.16026073899569804,0.1617241133930949,0.1649253084297686,0.16583830766574126,0.1672577518645979,0.1682028838249905,0.16861984873815627,0.1700288438481441,0.1711365896339525,0.17181744244892405,0.17596584502661594,0.17864756015520955,0.1826495877010017,0.19186895500596401,0.19709325323724736,0.20426987960839282,0.20909450179138878,0.22076465224222863,0.22832535793984965,0.23098641129864683,0.23697303994701846,0.24642682627665868,0.2553887084725175,0.2638895182684302,0.2723868034757708,0.2772642540457615,0.2796110380299166,0.28970594586271003,0.29246597837094557,0.29306759530835125,0.29353404984573706,0.2971187612669266,0.29757929214555245,0.29686277224723456,0.2907851435269202,0.29070940017486224,0.2905629190536705,0.28970594586271003,0.27779001564173056,0.27501433240858697,0.2723170849936287,0.268905233446024,0.26659742945724885,0.27090250275596306,0.280206784716277,0.28188053857395934,0.2850559977819809,0.28970594586271003,0.30961702256686907,0.3201690224299276,0.3389417738400744,0.35864723948319144,0.37151271651147466,0.38206494758634024,0.4064994348646285,0.42758853310367373,0.44355674788258304,0.4621928615979738,0.4820845761715842,0.49652982672415513,0.5236952604787635,0.56213623243787,0.5654711203446365,0.5661154763302831,0.5672700634217587,0.6096067925916198,0.6344124139651179,0.6549077346213079,0.7010353973554415,0.7025325760005336,0.7033537075855993,0.7055512191578583,0.7491449020072705,0.7722950012060816,0.7978622572256353,0.8255046156805705,0.841236294826563,0.8488829504161717,0.8776011238177879,0.901254102802413,0.9101775884470444,0.9261861750945317,0.9565417129629119,0.9791188820675258,1.008903303268824,1.0180931353932254,1.0480601756880072,1.0739992815961021,1.09476339898549,1.1170014693084895,1.131640456263732,1.1725192990643287,1.1828161213044468,1.185942762928971,1.1935145804084608,1.2315109055114246,1.2548840565494523,1.278477319465709,1.3237450403422923,1.3238253501699337,1.323852412183426,1.3239016477027934,1.3698655172923737,1.3927666437904151,1.4140690202313784,1.4481182867181457,1.4563318451332692,1.4617079374108974,1.4935173035435665,1.5293510213006374,1.5299618996024198,1.5306492310313788,1.558579104553051,1.5783025766789884,1.5847125243103632,1.5995905246518602,1.6052474181853262,1.6075540270301967,1.6092217806945217,1.6202657048581472,1.6261757854900423,1.628841141828611,1.6302228862281534,1.6348955096324178,1.6364914879041694,1.6367462959042043,1.638616966231233,1.64073581992518,1.6418373912831181,1.643500465347548,1.6466157231005574,1.6507762467470415,1.6531929571936295,1.655379002184135,1.6638777182862943,1.664682802797524,1.6650636418065772,1.6685318182723416,1.672587142848967,1.673138377140997,1.6732623119475512,1.676109458194437,1.6764904125514888,1.6767251774489913,1.680393971965573,1.6812842063804951,1.6836959069284743,1.6908906006874314,1.6960106729013549,1.7068113931027757,1.7109541018019274,1.7219173324653574,1.7272451167860923,1.737473111892823,1.7533035246220323,1.7640831570824935,1.7841146779529207,1.8064144055133053,1.8187510683058599,1.834804978648553,1.8604670348149805,1.8753556991337867,1.9086822734444877,1.9122727095638177,1.9442969927542681,1.9605128120505673,2.0083675167294834,2.0132382863747496,2.016416780870918,2.0351456419095197,2.0764861955544958,2.082179579995231,2.0898705945496316,2.137356268446313,2.1511208736157132,2.1711949236037644,2.1959855234415957,2.2200621672361947,2.2507652081702925,2.2620901241681186,2.289003460856676,2.3030250546016133,2.3330982909739606,2.349170471935358,2.3579447544771575,2.3883402826046294,2.4253234110770108,2.426041508602142,2.426886048097639,2.4555317008409703,2.4768686526041903,2.483416216812279,2.495827341718121,2.5079508419767715,2.5149897515096034,2.5316529881753778,2.5343977142206895,2.5499729418705894,2.554165104176874,2.5647686353386026,2.575426102981354,2.580871041337159,2.5856991722236917,2.589294688316745,2.593049635327938,2.5852600091052653,2.568113815402865,2.567287453014051,2.5660723565753103,0.9890357785260817,0.9791188820675258,0.9723554792472471,0.9629637911018043,0.968168461999936,0.9791188820675258,1.0074901971230301,1.0463077237605858,0.9890357785260817,1.881489813534151,1.8753556991337867,1.8681873734020287,1.8667304017205972,1.860955857633106,1.8496126346711788,1.8394728545071444,1.8277903828135185,1.8064144055133053,1.8038720676163797,1.8027784769462483,1.7995210775939356,1.782631681076157,1.7721345340564585,1.7628904493520792,1.752541318009874,1.7474501310129607,1.7457886949476502,1.737473111892823,1.7348262964172574,1.7343980511182555,1.7342122025374285,1.7309854320537972,1.7306317693175735,1.7305710585023024,1.7299196206766525,1.7298293102747038,1.729555164098652,1.72806546248512,1.7277939444881816,1.7265799704970326,1.7228167831429642,1.7215457024048946,1.7173363895995135,1.713270992654555,1.7092717481379025,1.6999861113662447,1.697459231561027,1.690513256914349,1.6848540359563668,1.6685318182723416,1.6671880250148123,1.6667579802734944,1.665734775412648,1.6501441120433413,1.6441412376569997,1.6325493137463645,1.6309088915830086,1.6210923447825984,1.6157254559597596,1.5995905246518602,1.5986027970928904,1.5983081258312448,1.5977357258826683,1.5837794055297088,1.5794758769749264,1.5706578374911655,1.5684510992537164,1.5607033083087933,1.5533544538047006,1.542093667672146,1.5393430028454742,1.5370617895360197,1.5306492310313788,1.5186445483267605,1.51421006931094,1.4973489538141318,1.496680409169493,1.4830996484512382,1.4762392781108775,1.4617079374108974,1.4535720496071813,1.4493000128714875,1.440107745550066,1.4330027120817754,1.4220586822993018,1.416308016201231,1.4092424611119125,1.404892576384714,1.4032738572383816,1.3945457043974145,1.3941788359386318,1.3940252050434983,1.3927666437904151,1.387232934758329,1.386642219602368,1.3859360591760779,1.3817693458375406,1.3808728572815272,1.3790808666771812,1.3781356143460077,1.3777951789167937,1.3772428371745176,1.3810702942021282,1.3810702942021282,1.3828179494603812,1.3927666437904151,1.3968731999538089,1.3981353364075475,1.405344668088612,1.418631733014195,1.42990031096581,1.4377086334676608,1.4478085304293118,1.4496471131885094,1.4268242864847518,1.4251463023730175,1.4051267496350452,1.3974497151935679,1.3927666437904151,1.3793717761443962,1.3493337720121557,1.3238253501699337,1.2976551501593092,1.27502103352511,1.2548840565494523,1.2372138563261381,1.2000571118271162,1.185942762928971,1.1557184851850635,1.1490735029522763,1.1170014693084895,1.1050005677843466,1.095971086990779,1.0705173938765138,1.0480601756880072,1.0366260345731093,1.0280453163626198,0.9996567058095152,0.9791188820675258,0.9613436212747746,0.9413081937929868,0.9215613468057753,0.9101775884470444,0.8805341729886584,0.846019450327637,0.841236294826563,0.8404586144964337,0.8395422828985502,0.8013979965904929,0.7722950012060816,0.7630748363618909,0.7529705257040704,0.7290505449366678,0.7033537075855993,0.696158942331428,0.6900286001886777,0.6750024887140937,0.6705073486136963,0.6514404058671928,0.6482222598724916,0.6356672452438583,0.6353058029566108,0.6352619692133001,0.6344124139651179,0.6317186789834159,0.6315703888621118,0.6315460209556876,0.6290403324990472,0.6288185839426004,0.6278059878398987,0.619323800324652,0.6166149199415245,0.607105156257338,0.603204364021876,0.5915281427744001,0.5825365917443137,0.5654711203446365,0.5587732637107723,0.5552653614482996,0.5348312638498869,0.5317355986873245,0.5088631035967546,0.503349261242604,0.49652982672415513,0.4724971628365293,0.45302090404698214,0.441686542055042,0.42758853310367373,0.41118919238959206,0.3983265160196532,0.3835633365587001,0.35864723948319144,0.3578903574998642,0.3574196134341432,0.3562993233474354,0.3367238741813634,0.32711654026665515,0.31428283481432073,0.2926577662488481,0.2914785347264295,0.2905961786961977,0.28970594586271003,0.28705823885711057,0.24497892053761783,0.22076465224222863,0.18844796344670955,0.18426520511208677,0.15182335862174723,0.12338961890386857,0.1132981985135526,0.08288206500126538,0.05593370868165426,0.036941145155257704,0.013940771380783978,0.0016712587897709241,-0.03916660801476324,-0.05101936310359534,-0.05500052223969787,-0.06246477738766831,-0.10174572498888335,-0.12394181586017927,-0.15355972037185106,-0.1673697821415283,-0.19288310948066067,-0.20537760921083326,-0.25028756095804594,-0.25902878251003436,-0.2618244031011425,-0.2665015620136266,-0.3129525350442597,-0.3307656967216239,-0.35891361296467883,-0.36909375581792636,-0.3997069903421058,-0.42614640979114826,-0.44548145353768875,-0.4686482839625872,-0.4846101803704621,-0.5284500551245288,-0.5375895775830686,-0.5441912635091812,-0.5890009761556345,-0.6036529035335687,-0.6065308712035504,-0.6106973467631476,-0.6616981071552326,-0.6754721648240318,-0.6952120933337707,-0.7201222875745454,-0.7444134584445137,-0.7787502918418836,-0.7789782071357738,-0.8133547520649951,-0.838261912586336,-0.8606919877656947,-0.8822960456854769,-0.8985638817923363,-0.9399546103729159,-0.9512373393059583,-0.9603471968441895,-1.0157311253693755,-1.0201786329264397,-1.024101812312935,-1.0879213589501422,-1.0891199265469216,-1.0903065144404436,-1.1569457785289234,-1.158061220167403,-1.159250904497544,-1.223458606293244,-1.2270025137878848,-1.2310566541466663,-1.2882575840070492,-1.2959438074083662,-1.3051340472708928,-1.3523324827103238,-1.3648851010288476,-1.3799338694518708,-1.4168939793475364,-1.4338263946493295,-1.45305723422132,-1.4836025082575426,-1.5027676882698109,-1.5210779118550453,-1.5559759756922018,-1.5717089818902927,-1.58558445174152,-1.6331413394330183,-1.6406502755107741,-1.6470381024409315,-1.6921398435924662,-1.7068655011023184,-1.7095915691312555,-1.713141438269885,-1.7715692260400697,-1.7785328627517374,-1.7848173387761381,-1.8211835406307357,-1.8435476416094403,-1.8474741563722188,-1.8575911912523897,-1.8902650701631494,-1.9164154499927004,-1.9325179376921242,-1.9512308460082406,-1.9659802900857204,-1.985356743613182,-1.9942680635168106,-1.9994930175989385,-2.0028639405278557,-2.0089622691063402,-2.014135163166371,-2.0093061717442198,-2.0039917664797375,-2.0010107250528617,-1.9951664676485938,-1.985356743613182,-1.9687132031727732,-1.9580681502336823,-1.9374602297111545,-1.9164154499927004,-1.9033603679685385,-1.8905941977028888,-1.8673501119167706,-1.8474741563722188,-1.8300388383669062,-1.809266163137559,-1.7914211264351017,-1.7785328627517374,-1.7491471797055764,-1.7242981923331153,-1.7095915691312555,-1.705942884883204,-1.6980164559240443,-1.657092994404283,-1.6406502755107741,-1.610843891455891,-1.6036693754852531,-1.5717089818902927,-1.5484510924986772,-1.5211871038268385,-1.5027676882698109,-1.4909933850973323,-1.4345204928954534,-1.4338263946493295,-1.4334127127757705,-1.4320011624755948,-1.3828213840087984,-1.3648851010288476,-1.3369924373655442,-1.3045811667612157,-1.2959438074083662,-1.294041891533681,-1.2918231761734909,-1.2600578133074598,-1.2270025137878848,-1.2263233709935117,-1.2257534054596015,-1.2193225761229778,-1.1953429963952984,-1.1696965515016826,-1.1643254537882926,-1.158061220167403,-1.1312480919770014,-1.10607326643116,-1.0975498544916613,-1.0891199265469216,-1.061085752331084,-1.0285288356480757,-1.0238944679404174,-1.0201786329264397,-0.9986485403129088,-0.9836905441999435,-0.9512373393059583,-0.9434448597868008,-0.931291997517917,-0.9003407383577784,-0.8822960456854769,-0.8550174826276375,-0.8273474126337725,-0.8133547520649951,-0.8090131062339658,-0.7992736956868685,-0.7608252902944037,-0.7444134584445137,-0.7106096616134265,-0.7096515773805749,-0.6754721648240318,-0.6586491309781808,-0.6103127621167084,-0.6065308712035504,-0.6045278451606286,-0.5958423633213399,-0.5498291622121809,-0.5375895775830686,-0.5186559030807874,-0.49348185054896465,-0.4686482839625872,-0.43615958283716605,-0.43133445007258864,-0.3997069903421058,-0.3792252768607085,-0.3441276410227685,-0.3307656967216239,-0.3227276293676611,-0.29212900530979447,-0.2693449124857663,-0.2618244031011425,-0.24587970940722403,-0.2199181608101064,-0.19288310948066067,-0.17227365481924295,-0.12869996833683706,-0.1256352557914444,-0.12394181586017927,-0.11821173851371158,-0.08246329160572019,-0.05500052223969787,-0.039080480629839265,-0.010484114650699095,0.004680817397714865,0.013940771380783978,0.0439601739753237,0.04960675932714054,0.08288206500126538,0.09411554252257215,0.11817261056583295,0.13970295184328707,0.15182335862174723,0.1851967360829918,0.1895694859959769,0.22076465224222863,0.23013075175482767,0.2480341948126985,0.27112717811806286,0.28970594586271003,0.30838280460765555,0.32922226929395526,0.34040467212401593,0.35864723948319144,0.36622974660328156,0.3705345241318718,0.3789139057589508,0.38613173407278056,0.39549356136911795,0.4044564001395412,0.41880083679384006,0.4214073682401005,0.4231840445909909,0.42758853310367373,0.4439346503079009,0.4511035101654728,0.46418585800635226,0.467074705495214,0.4777983997547275,0.48157960118090104,0.49479662783614176,0.4952008472947411,0.49538774878183167,0.49652982672415513,0.504640208309056,0.5058881348195112,0.5085284997589157,0.5152484755594533,0.518539312733918,0.5301985253213961,0.5305445202308481,0.5399005076790542,0.5481905160967693,0.5654711203446365,0.571423976991627,0.5750824132663284,0.6009315107332331,0.6076360781742838,0.6273241033398738,0.6299075856067122,0.6344124139651179,0.656855777452654,0.6716107235505526,0.6716107235505526,0.6707634430471283,0.6669340076069363,0.6571935492798224,0.6397310816955204,0.6367335700073489,0.6358907035318695,0.6344124139651179,0.614106021365846,0.6048530180384994,0.5954065340859294,0.5912245678389119,0.5810309813735279,0.5791673406788083,0.5726233633264521,0.5713638601354893,0.5725688734986325,0.5794865151094757,0.5815136369348219,0.6006884253330784,0.6026565077489869,0.619174995427842,0.6266703153541511,0.6344124139651179,0.6640739989392039,0.7014481242855068,0.702627894738217,0.7033537075855993,0.7053071618259641,0.750639655529834,0.7722950012060816,0.8031060294522665,0.8126022394697467,0.841236294826563,0.8620586194477773,0.8911922895533366,0.9101775884470444,0.9325545079227431,0.9546771538790915,0.9791188820675258,1.0120932144972392,1.0162515981297617,1.0480601756880072,1.066495792205401,1.1153447595684667,1.1170014693084895,1.1178394634014466,1.120042275520699,1.167513319083811,1.185942762928971,1.2153510582757234,1.2346110629876024,1.2548840565494523,1.2619029424514117,1.2734961919305543,1.301251270274268,1.3238253501699337,1.336940061375175,1.3484893682735613,1.3613340545809218,1.3655327957805885,1.378013769634213,1.3791661383577627,1.3830301862456715,1.3840663139828862,1.3834216613256038,1.3814465628814676,1.3809834307338984,1.3800209172599485,1.37961746694998,1.3794942268956727,1.3800343478191661,1.3828612373610327,1.3828612373610327,1.3838483537480246,1.390208862592679,1.390396658246973,1.390844006467947,1.3927666437904151,1.4019822533046518,1.4036965800328578,1.408266034851907,1.418557533348228,1.4281567079278985,1.4390876829575503,1.461250955516881,1.4615033376847628,1.4615763843370515,1.4617079374108974,1.4845137405110127,1.495877921176635,1.506248668228904,1.5211361472805236,1.525427902606498,1.526704636061671,1.5306492310313788,1.5448615563216612,1.5500948485277406,1.560213661175942,1.5622399118195873,1.5704609669691583,1.5779119671219894,1.5913104524216348,1.5930910555503632,1.595104364007987,1.5995905246518602,1.6210044590033426,1.6348812332465275,1.650625911913369,1.6685318182723416,1.6851867612782443,1.7049765993673858,1.721752361389767,1.737473111892823,1.7589922901023356,1.786281315059807,1.7947486085078102,1.8064144055133053,1.8254086154051792,1.8416535587041127,1.845864490525463,1.8475233390383656,1.8599418537946986,1.8611797265729275,1.865063175490222,1.86893668155319,1.8697361169931699,1.8753556991337867,1.87923010275632,1.8792978174635961,1.8792978174635953,1.887043826380403,1.8873974476794335,1.8869506902564113,1.8851172394586766,1.8833369569334661,1.881489813534151,0.9179119733818868,0.9101775884470444,0.903001595038122,0.88276174496843,0.864172689588901,0.841236294826563,0.8371293517815697,0.8358889071830187,0.8383773246281376,0.841236294826563,0.8473992441405884,0.8964417994365088,0.9101775884470444,0.9209837130305538,0.9441039354253475,0.9464278786856446,0.9480355912713248,0.9480355912713239,0.9179119733818868,1.681399130770949,1.6685318182723416,1.661273541716938,1.6584913485598602,1.653513704327993,1.6446984104886027,1.6377160214708657,1.631730150007725,1.6306631372292952,1.6257761589515956,1.6241918065108796,1.6228331063850177,1.6216788069837462,1.621379720338258,1.6210267344442033,1.6208618582197727,1.6200260123525632,1.6188289262183368,1.618238392518561,1.6161636435798017,1.611041291617767,1.6098854789864183,1.607951980490864,1.5995905246518602,1.595013567503114,1.593957884431528,1.5909546676237318,1.5785033514031404,1.5718084332723294,1.5604923126993309,1.5548393526870377,1.5462961963522983,1.5421007768397064,1.5306492310313788,1.523688061827817,1.521173536121625,1.5164612980203702,1.5064312715777262,1.4984763482915553,1.4896529429151122,1.483630603968623,1.4769334599558541,1.4732968867052914,1.4617079374108974,1.4568184994356064,1.4552792665345886,1.451447353858129,1.4391068471027366,1.4313764744024193,1.419035116032806,1.4044985829540013,1.3996418473046126,1.3971018528493278,1.3927666437904151,1.3694490371886636,1.3534052761811943,1.3401057649618395,1.3238253501699337,1.3072100478051127,1.2900801112626383,1.2735324176821456,1.2548840565494523,1.2394267016563005,1.222137848841681,1.209044389541686,1.185942762928971,1.1838379989852927,1.1823490267459316,1.1823490267459316,1.1785069573978917,1.1781316822688415,1.1791912975851973,1.185942762928971,1.1879398333217863,1.1881720482947737,1.1881720482947737,1.1897068276070804,1.1897512685059275,1.189121941508525,1.185942762928971,1.1751873855522539,1.1722172005782627,1.1475871888047533,1.1170014693084895,1.1167373696540266,1.1161028055176376,1.06210418729917,1.0480601756880072,1.0324497850113983,0.988910620334027,0.9791188820675258,0.9738120518529665,0.962189202159736,0.9293553852925451,0.9101775884470444,0.8906244287839793,0.8705113632382564,0.8604760957807218,0.841236294826563,0.8375581496268008,0.8360774037335692,0.8355261201659503,0.8311170990693326,0.8302770664573669,0.8308761083022538,0.8340360252159296,0.8340360252159296,0.8329068410899043,0.8297493182903213,0.8290109876805283,0.8188191734364989,0.8114754632404515,0.7984377921103829,0.7870119395245614,0.7722950012060816,0.758457754517194,0.7495235807295173,0.7296775766397103,0.7033537075855993,0.7001805678878861,0.6979569551251283,0.6788386112523166,0.6702025377617011,0.6448104985998477,0.6402334677805821,0.6344124139651179,0.6093191961973514,0.5887577670734854,0.5793653530123248,0.5654711203446365,0.5519788657204763,0.543310669496972,0.5331853636048334,0.5322201008242291,0.5227926348536518,0.5231439701353504,0.5227400498768255,0.5227400498768255,0.5242372568892422,0.5237032919907016,0.5237032919907016,0.5147695434665471,0.49652982672415513,0.4904702080399512,0.4855099112903143,0.4428419624595201,0.42758853310367373,0.4068821322905758,0.3839859053363699,0.35864723948319144,0.3285054959336793,0.32053543643794624,0.28970594586271003,0.2601049398968107,0.25005107917304636,0.22076465224222863,0.19883617325491842,0.16990485362669583,0.15182335862174723,0.13999895373921412,0.08455154101399698,0.08322004578142872,0.08288206500126538,0.08230293429002034,0.03096521670399799,0.013940771380783978,-0.0198314295573625,-0.02085373872413454,-0.05500052223969787,-0.07120177623562896,-0.11436164040261598,-0.12120640769710445,-0.12394181586017927,-0.12985993062539203,-0.17059948616564613,-0.19288310948066067,-0.22113497097054724,-0.23982800467809096,-0.2618244031011425,-0.27235034453580553,-0.30791553583967524,-0.32544476629976504,-0.3307656967216239,-0.33951401252760194,-0.38061127926890626,-0.3997069903421058,-0.42856337299777403,-0.43793621131199734,-0.4686482839625872,-0.4967922824548947,-0.5115447343196871,-0.5375895775830686,-0.5573678355717431,-0.5908235866945373,-0.6065308712035504,-0.6191332712031548,-0.6683367567345893,-0.6754721648240318,-0.6813648615043326,-0.7353192161927495,-0.7433676830066007,-0.7444134584445137,-0.7457882233842152,-0.8044626915401993,-0.8133547520649951,-0.8248742929438682,-0.8659074334129495,-0.8822960456854769,-0.9027742041799729,-0.9283514035490996,-0.9512373393059583,-0.9781030030865012,-0.9925214402159259,-1.0201786329264397,-1.0500934861281959,-1.0591268100048348,-1.0891199265469216,-1.1183614244316007,-1.1291944403920997,-1.158061220167403,-1.1845374332095253,-1.2017442770776916,-1.2270025137878848,-1.2486924753163269,-1.27713050745086,-1.2959438074083662,-1.311272537976215,-1.355149896114515,-1.3648851010288476,-1.3725546671350237,-1.4246077361059974,-1.4325225813478468,-1.4338263946493295,-1.43591309172208,-1.490660441767445,-1.5027676882698109,-1.5237547957972652,-1.5464454591173822,-1.5717089818902927,-1.6002540109353003,-1.6188685885482332,-1.6406502755107741,-1.6528895942063686,-1.6807268921804472,-1.6916648171777586,-1.7095915691312555,-1.7158350176036303,-1.7183678769176853,-1.7158538852587077,-1.7095915691312555,-1.6978698152335596,-1.6939838500941948,-1.6687409538142575,-1.6406502755107741,-1.6359537407472668,-1.631447023503719,-1.5940581394243432,-1.5717089818902927,-1.5482848605548662,-1.5102753561150069,-1.5027676882698109,-1.499888055413742,-1.491572624600849,-1.4464867286674568,-1.4338263946493295,-1.411305964302617,-1.3929100632177924,-1.3648851010288476,-1.3417681247812707,-1.3034619844162245,-1.2959438074083662,-1.2930945547617716,-1.2883626265973902,-1.251966590831311,-1.2270025137878848,-1.2132103227721354,-1.1986472781299677,-1.1791166390209487,-1.158061220167403,-1.1465599041672596,-1.1368940519280084,-1.1146918556521213,-1.0891199265469216,-1.0823398832221005,-1.0758982383985152,-1.0476133644872223,-1.0201786329264397,-1.0120334029975044,-1.0022062815636579,-0.9742802891888251,-0.9512373393059583,-0.9358746963549054,-0.9153911355346778,-0.896569663434287,-0.8822960456854769,-0.8567860870244846,-0.8212896488812103,-0.8165213675347966,-0.8133547520649951,-0.8006668421082068,-0.7741275923327424,-0.7444134584445137,-0.731291894085655,-0.706843934072777,-0.6856697145408455,-0.6754721648240318,-0.6523240934056878,-0.6364368041433446,-0.6065308712035504,-0.5860911863836398,-0.5467103681031653,-0.5375895775830686,-0.5328554685196325,-0.5127282942504725,-0.4775458111453954,-0.4686482839625872,-0.4549951575285114,-0.42103487657754224,-0.3997069903421058,-0.36708109369378583,-0.3640853941322977,-0.3307656967216239,-0.30843650121465727,-0.2760722533324973,-0.2618244031011425,-0.2540836552433099,-0.23080798666857083,-0.20352724412469048,-0.19288310948066067,-0.16569551294620632,-0.15591101895708803,-0.12394181586017927,-0.11007921075955762,-0.08440969598011483,-0.0659684738029922,-0.05500052223969787,-0.02241649456363959,-0.013453964362444282,0.013940771380783978,0.020626258435129774,0.03248939139457585,0.06425314145294792,0.08288206500126538,0.10937550269898688,0.14045530566196485,0.15182335862174723,0.1555362730529608,0.16401539033330836,0.20235996297476033,0.22076465224222863,0.24998716515472585,0.26830762917651496,0.28970594586271003,0.29792038023878886,0.3165547903786128,0.34322335660866665,0.35864723948319144,0.3857015409081259,0.4274247525780974,0.4275063655984268,0.42758853310367373,0.46043114063082635,0.4904484804163691,0.4927863457246642,0.49652982672415513,0.5202036428929424,0.5359777183958889,0.5476128616760509,0.5654711203446365,0.5760450118289282,0.5845803642507224,0.6074324681046677,0.6344124139651179,0.6396513426917836,0.6452882978025936,0.6713613198188386,0.693193288082322,0.7013937387278042,0.7019613646685747,0.7033537075855993,0.721670486289772,0.7289932135705457,0.7318703266844149,0.7333971919696292,0.7378159871891232,0.743960105384383,0.7473578032861767,0.7520764660233898,0.7593888800952411,0.7722950012060816,0.7865617736148782,0.7972803096811654,0.8231621290018452,0.841236294826563,0.8682932347379775,0.8935749446139485,0.9101775884470444,0.9167311480502849,0.940760817705367,0.9712183388934039,0.9791188820675258,0.9907151378301973,1.0303442957467568,1.0480601756880072,1.0694725770602056,1.0953481167144896,1.1170014693084895,1.1353081153872462,1.175408742056573,1.185942762928971,1.1922346600749552,1.205567670325053,1.2388293995651067,1.2548840565494523,1.2788621683234838,1.3060345864711596,1.3138742507751382,1.3238253501699337,1.3411609990567306,1.351515585472797,1.3606508456727275,1.3625230521123606,1.3708136864852674,1.3702759879592947,1.3707629038571008,1.3707629038571008,1.3663784270789283,1.3648210366756204,1.3618415870550948,1.362785925327119,1.3630779735196783,1.3632090059216107,1.371910985370301,1.3914075262026944,1.392005048252082,1.3923738653075222,1.3927666437904151,1.4257488354890087,1.4566986516933311,1.459586530717114,1.4617079374108974,1.4835618531770431,1.4976414625791068,1.5306492310313788,1.535746943201009,1.5412912493136415,1.57178641793362,1.5995905246518602,1.60704969546337,1.6137310822409234,1.6368990316967174,1.6524332709378196,1.6653691174094685,1.6665340388202803,1.6685318182723416,1.6914693231255575,1.7044345804737495,1.7122995730127237,1.7207487729701865,1.7276627675484906,1.7288056825905609,1.7366442976569725,1.7368113735608905,1.7367775775167682,1.7325548812822036,1.7322269323739117,1.730224479750349,1.719186205304395,1.7145357644998485,1.7010373207301313,1.6982461060581202,1.686940205552069,1.681399130770949,1.619137678006585,1.5995905246518602,1.599319074917466,1.599216141062421,1.5989131408352244,1.5794745632628975,1.5713532270736192,1.5604902503227236,1.555190279475268,1.5474149202505063,1.5443621453891043,1.5324732420904907,1.532148554124913,1.532019173928735,1.5306492310313788,1.5258091057748504,1.5253233301020193,1.5249043272662397,1.5229641103012743,1.522695501749293,1.521990644528373,1.5190900346411422,1.518401892123546,1.5158182895713623,1.5104923744696523,1.5073305878885654,1.497506790506256,1.496926776453503,1.487506861449822,1.4803911538908703,1.4617079374108974,1.461348799624313,1.4611959294993393,1.4608356976594128,1.4408220819902442,1.4319629648244523,1.4215216829009267,1.4150043669020484,1.4066151203741017,1.4032177108621355,1.3927666437904151,1.38588369895163,1.3834489519245898,1.3789367193781508,1.3684628941359125,1.360200223072718,1.3507538188723172,1.342603012318531,1.3359750338187104,1.3323457203411375,1.3238253501699337,1.3100801937951494,1.3029969974511517,1.2830385255339958,1.2548840565494523,1.2543529014847636,1.2538299589374433,1.2158481214775825,1.185942762928971,1.175479712068808,1.153700567271645,1.1287805931124981,1.1170014693084895,1.0945548722466891,1.0739591293924193,1.0480601756880072,1.0221564759739024,1.0015774256871288,0.9791188820675258,0.965111899054675,0.9372465046592722,0.9207902960240006,0.9101775884470444,0.8847927562900755,0.8601030748154348,0.852654280742088,0.841236294826563,0.8259363503680404,0.8164671984093608,0.802258413658,0.794128443970544,0.7843002367326739,0.7814436076620006,0.7722950012060816,0.7648652092795367,0.7624717570410193,0.761981899590515,0.7556002322011417,0.7530595270712026,0.7530595270712026,0.7509667908793944,0.7502237359887087,0.748556042170994,0.7465885627881046,0.7439943302808856,0.7336607863331843,0.7293526441855112,0.7220129320603657,0.7136982723548733,0.7033537075855993,0.6756321825941485,0.6371206644157419,0.6344124139651179,0.6338263680878558,0.631151361563028,0.5726882258399901,0.5654711203446365,0.5580160716964131,0.503185996832872,0.49652982672415513,0.49150549014689515,0.44048101216520186,0.4289736537347557,0.42758853310367373,0.4261297788976681,0.36904150753973264,0.35864723948319144,0.34567649066584094,0.30920740324941187,0.28970594586271003,0.2633683785489853,0.24976073184219727,0.22076465224222863,0.19156923602460152,0.17879370572027087,0.15182335862174723,0.1343009026020412,0.09114225591477387,0.08288206500126538,0.07775960553027117,0.05714454264977942,0.02367180189829421,0.013940771380783978,-0.004624344279703596,-0.02868131466985746,-0.05500052223969787,-0.08004901530302622,-0.10962770601002392,-0.12394181586017927,-0.13060572849328578,-0.1475250734763045,-0.17967412163356133,-0.19288310948066067,-0.2233790740710604,-0.22903738297912923,-0.2618244031011425,-0.27868683038864983,-0.32594832045027866,-0.32955145498279315,-0.3307656967216239,-0.3329158507270318,-0.38350150872801736,-0.3997069903421058,-0.42528195193276597,-0.43999327170416347,-0.4686482839625872,-0.4987230617136129,-0.508946664618747,-0.5375895775830686,-0.559952747782031,-0.5868883728181951,-0.6065308712035504,-0.6232878325825562,-0.6616932277879704,-0.6754721648240318,-0.6878528594075113,-0.7353362304835351,-0.7444134584445137,-0.7527452976103097,-0.8089787735556571,-0.8133547520649951,-0.817427751084653,-0.8775080449576262,-0.8819827223957937,-0.8822960456854769,-0.8826626327430298,-0.9476329552663061,-0.9512373393059583,-0.955224938453072,-1.0154103432090085,-1.0201786329264397,-1.0249044692848956,-1.0862699452524258,-1.0891199265469216,-1.0917842079442028,-1.1300092983743943,-1.155630524969781,-1.158061220167403,-1.1614923423736978,-1.2155851807877887,-1.2270025137878848,-1.244864469847498,-1.2724563928885124,-1.2959438074083662,-1.3264660443815193,-1.3382932173266355,-1.3648851010288476,-1.378292254141404,-1.4091892602871168,-1.4130106587807956,-1.419151628558312,-1.4231797003882658,-1.387964317983109,-1.3648851010288476,-1.346806046512771,-1.3209832827840269,-1.303223821695795,-1.2959438074083662,-1.2699679295495678,-1.2590130278358869,-1.2270025137878848,-1.2166955609448884,-1.2048793374621298,-1.179279766383221,-1.158061220167403,-1.143944437453123,-1.131503747141498,-1.111958719789238,-1.0891199265469216,-1.0806230249322102,-1.0740103165744612,-1.0490688718672057,-1.0201786329264397,-1.0169945257045963,-1.014014995735522,-0.9813004835256538,-0.9512373393059583,-0.9450331539276084,-0.9374069240104825,-0.9063655467433933,-0.8822960456854769,-0.8673652120441804,-0.8475974716569352,-0.8282800610726158,-0.8133547520649951,-0.7895774207214652,-0.7593552342535439,-0.7508066138338045,-0.7444134584445137,-0.7101660747547109,-0.7087405865849856,-0.6754721648240318,-0.6697719261014283,-0.6605420053350546,-0.6253014188388559,-0.6065308712035504,-0.5774406559115808,-0.5600571455309131,-0.5375895775830686,-0.5280751564885833,-0.49670168145871063,-0.4750431361533374,-0.4686482839625872,-0.45823840255569737,-0.4197567186738951,-0.3997069903421058,-0.3681413023897888,-0.36344759627085876,-0.3307656967216239,-0.3078625996522275,-0.27726795016346095,-0.2618244031011425,-0.25315073237310326,-0.22548490790883857,-0.20138522240171408,-0.19288310948066067,-0.1727064080696401,-0.1528987319758377,-0.12394181586017927,-0.1060452735647548,-0.07142724430383529,-0.06094254518695319,-0.05500052223969787,-0.03264276658047738,-0.01753236461810559,0.013940771380783978,0.025648107853915914,0.04587984955666702,0.0690659731384482,0.08288206500126538,0.11381775392903304,0.1284191643904693,0.15182335862174723,0.1592501229069314,0.1755805320894681,0.20640254982664752,0.22076465224222863,0.2549398612705551,0.25592665609655674,0.28970594586271003,0.30410413193603025,0.3413490285466074,0.35337627808897976,0.35864723948319144,0.3732273402442483,0.40046858557644915,0.42758853310367373,0.4466126580439247,0.48170525273574816,0.49030916049225715,0.49652982672415513,0.5286972737972335,0.5529413899739954,0.5654711203446365,0.5667924349301816,0.5683377374498373,0.600334296307167,0.6124017739308729,0.6329721741119756,0.6336273407647881,0.6344124139651179,0.6687093575583742,0.6773533946977559,0.7033537075855993,0.7038722987432657,0.7045951514221795,0.7441608007538547,0.7722950012060816,0.7861907688501222,0.8141518318075796,0.830911639873793,0.841236294826563,0.8728801028233799,0.8767344285984024,0.9101775884470444,0.9253925403405945,0.9749568809724294,0.9774081811474784,0.9791188820675258,0.983711139924742,1.0340210877993097,1.0480601756880072,1.0581567153378821,1.0736521848577198,1.1065749624122225,1.1170014693084895,1.1460336313912518,1.1782279528952135,1.183158007767569,1.185942762928971,1.2123186207622916,1.2212360223921208,1.2548840565494523,1.2588328675694656,1.2628266526533545,1.2998023097823554,1.3238253501699337,1.3407657463214133,1.3639649639690714,1.382286249689837,1.3927666437904151,1.4236741159974682,1.4472331169623565,1.4617079374108974,1.46459772454399,1.4682163239059727,1.5023879174558314,1.5306492310313788,1.539160188137402,1.5473955697313246,1.5697077062982303,1.5967499880776388,1.5990194152709436,1.5992090920995827,1.5995905246518602,1.6216378241088578,1.6322636396330243,1.6377863124133527,1.6394175910623603,1.646477569772601,1.645930632069558,1.6450316947638348,1.644106775648527,1.6354966942464135,1.6349489287859043,1.6270310084023403,1.619137678006585,1.5468524546238647,1.5306492310313788,1.5265535244042838,1.5248455735161701,1.5190298742814572,1.5047070533185267,1.4928661349449261,1.4834553029347242,1.4640435836421513,1.46316139938908,1.4628282901960845,1.4617079374108974,1.4451325880973225,1.4393457989455585,1.4309071199641408,1.429738708089236,1.4236859236088173,1.419643996938579,1.4169559336175488,1.4148221876660148,1.4123618002791072,1.4080898467390495,1.4065942381294447,1.4041661029411654,1.3927666437904151,1.391882994232795,1.3916343762313912,1.3908644417483065,1.3713010573411375,1.362086503445337,1.34982897548173,1.3347287255479858,1.3292824179014837,1.3276212241733014,1.3238253501699337,1.3040271656358144,1.2933391347563927,1.2822456649639862,1.2725501608220955,1.264630101794301,1.2619920960011606,1.2548840565494523,1.239837931593636,1.231645843614713,1.2158207322367374,1.2054769810420862,1.194711560751545,1.1915385499025892,1.185942762928971,1.1563498352754693,1.1196835242041527,1.1180985455329453,1.1170014693084895,1.1154494546721936,1.1075370220911256,1.0612316754308524,1.0480601756880072,1.0264965348910216,1.0112306882501172,0.9984239028109099,0.9791188820675258,0.9728916584030372,0.9701815089081607,0.9657230107247954,0.9542870377939878,0.945041084785998,0.9383258507863173,0.934364087615402,0.9278750295127938,0.9248301493925548,0.914432948335937,0.9135622093358493,0.9128232046663007,0.9101775884470444,0.8979834111292218,0.8946516372205751,0.8728636991243337,0.8602718794899169,0.8491203655097483,0.8444294564131751,0.841236294826563,0.8340416607523644,0.7962484269679462,0.7722950012060816,0.7395275896028548,0.7359463949792882,0.7033537075855993,0.6787178779235421,0.6607846796860328,0.6344124139651179,0.6059619132252192,0.5958520023909384,0.5654711203446365,0.5372640608460499,0.5223259729521224,0.49652982672415513,0.4807302835678917,0.433306456608904,0.42758853310367373,0.4242615800450955,0.4096874139971374,0.3682647203594871,0.35864723948319144,0.3445209270038414,0.3113280337650335,0.28970594586271003,0.25753993926648944,0.2537431769874643,0.22076465224222863,0.19646703641845642,0.17135978749130976,0.15182335862174723,0.1388827546778395,0.0848943673615068,0.08288206500126538,0.08154875544347417,0.0753087076517569,0.02578918337946856,0.013940771380783978,-0.0064076902681944325,-0.02895771297439964,-0.05500052223969787,-0.08276108288667983,-0.10216583259120915,-0.12394181586017927,-0.13582184150714127,-0.17073193621840188,-0.1868213781148027,-0.19288310948066067,-0.20702404483069126,-0.23623937733317701,-0.2618244031011425,-0.28564750106513515,-0.32109441189596355,-0.3307656967216239,-0.3351823484574088,-0.3477069614306454,-0.38728199990365164,-0.3997069903421058,-0.4208184771820864,-0.4424796501555006,-0.4686482839625872,-0.5005095490401348,-0.5066544257227621,-0.5375895775830686,-0.5620007236831888,-0.5840010614439337,-0.6065308712035504,-0.6270738097793851,-0.656123606979373,-0.6754721648240318,-0.695471447451157,-0.7249826863228943,-0.7444134584445137,-0.7653577762189472,-0.7926883945512513,-0.8133547520649951,-0.8368718153268309,-0.8586996865761845,-0.8822960456854769,-0.9115466081055295,-0.9215478128057364,-0.9512373393059583,-0.9804329155171434,-0.9955004255402451,-1.0201786329264397,-1.0350398745982816,-1.068182974705818,-1.070260668227124,-1.074126300677336,-1.0813218632464112,-1.0781016533359944,-1.0625046184628681,-1.04924526932774,-1.0380151119177277,-1.0201786329264397,-1.0120458388955966,-1.0075288281043218,-0.9836102682927472,-0.9717408104566454,-0.9562132893888089,-0.9538051271150891,-0.9512373393059583,-0.9189027954320261,-0.8855005461838763,-0.8837419538166573,-0.8822960456854769,-0.8698283026822513,-0.845194386944486,-0.8133547520649951,-0.8067891991133775,-0.7989483782148126,-0.7687449652688776,-0.7444134584445137,-0.7311014072599278,-0.7159507460385135,-0.6936803558643798,-0.6754721648240318,-0.6553409311611871,-0.6295522769173534,-0.6156827772992686,-0.6065308712035504,-0.5749925210107567,-0.5712467500620573,-0.5375895775830686,-0.5261060290470461,-0.49841436381711723,-0.47658055544162004,-0.4686482839625872,-0.4542368977336033,-0.42329860253893825,-0.3997069903421058,-0.36856510280851396,-0.3599027576554352,-0.3307656967216239,-0.3135750126370498,-0.2674128141006009,-0.2618244031011425,-0.25866096659588145,-0.2482227439238205,-0.20625455673860404,-0.19288310948066067,-0.16347949107540716,-0.15620428626676608,-0.12394181586017927,-0.10777163262706635,-0.07438121802762021,-0.061656058664685265,-0.05500052223969787,-0.031411026459090774,-0.01754475302380598,0.013940771380783978,0.02633073943299946,0.04784103447098165,0.06986967978770453,0.08288206500126538,0.11435800773176918,0.12717442921691147,0.15182335862174723,0.15966726275446375,0.17661875569286556,0.20679986469848588,0.22076465224222863,0.2547252065612384,0.25546059252320363,0.28970594586271003,0.3054435956786219,0.3489270841923928,0.356007667814215,0.35864723948319144,0.3646866402165636,0.4062295007003409,0.42758853310367373,0.45506727437665395,0.4802616387349432,0.49652982672415513,0.502879791878414,0.5150518451072874,0.5466078968546646,0.5654711203446365,0.5883021875005237,0.6209396257005708,0.6282013493852143,0.6344124139651179,0.6655729673592243,0.702552463085095,0.7029641760182126,0.7033537075855993,0.7065310247755998,0.7415117644972322,0.7722950012060816,0.7811653275461725,0.7969195895885144,0.8252572810591476,0.841236294826563,0.8744125438957853,0.87824668840272,0.9101775884470444,0.927672845070068,0.9670542815000203,0.9791188820675258,0.9894970392386395,1.0351465742925225,1.0480601756880072,1.066474382290131,1.0921465465331246,1.1170014693084895,1.1431442813478703,1.1733090151466592,1.185942762928971,1.1904870850261093,1.198214082750423,1.2375928417287185,1.2548840565494523,1.2833996765613045,1.3095773792680814,1.3238253501699337,1.3281160609786746,1.3350474917953261,1.3719281630866234,1.3927666437904151,1.4137974080377584,1.4427096117549296,1.4530532231214388,1.4617079374108974,1.4876722984736461,1.5125663949573105,1.519555580690096,1.5306492310313788,1.5452419939515551,1.5535452604458935,1.5604736596567848,1.5625727402598835,1.5718882838224366,1.5717790505011782,1.571504873026663,1.5709145361708035,1.5625703273656257,1.560765680208124,1.5536154453799438,1.5468524546238647,1.4786874459007229,1.4617079374108974,1.4570225924547464,1.45477190899418,1.4448735899400167,1.432390947475373,1.416333281542752,1.4079938380331192,1.3927666437904151,1.3822619646775167,1.3750991490453965,1.3550472683783963,1.3433833651908702,1.3322547379413225,1.3295003354753878,1.3238253501699337,1.3004780901981818,1.2811667741668589,1.2709593682138505,1.2548840565494523,1.237480773454847,1.2076298081169115,1.1963097636688507,1.185942762928971,1.166081567635898,1.139865627639884,1.1170014693084895,1.09907161818678,1.0557358142462605,1.0480601756880072,1.0445605596561776,1.0304546307972253,0.9841901244358655,0.9791188820675258,0.9738514424866715,0.9196013568495922,0.9101775884470444,0.9006616138110242,0.852186888530436,0.841236294826563,0.8310737237476418,0.7811033514714505,0.7722950012060816,0.7650298437419267,0.7048630653931887,0.7033537075855993,0.7022466350153898,0.6960357129486723,0.6438330024437628,0.6344124139651179,0.6207066245775388,0.5875942984364086,0.5654711203446365,0.5328760690021981,0.5277805950338368,0.49652982672415513,0.4799535173324938,0.4286451622891234,0.42758853310367373,0.4270485819032257,0.4252846684690996,0.3732693361562318,0.35864723948319144,0.33450367110948376,0.31807190854732914,0.28970594586271003,0.26226988632949544,0.24438768329931504,0.22076465224222863,0.20556306147606174,0.15720687875921824,0.15182335862174723,0.1482058634374792,0.12968119205995965,0.09054650485912319,0.08288206500126538,0.07122601686598529,0.03286622896214375,0.013940771380783978,-0.015083903089708084,-0.024287058493055902,-0.05500052223969787,-0.08133082724406071,-0.10269118532259425,-0.12394181586017927,-0.13781577788616772,-0.19179748242945527,-0.19263888365726345,-0.19288310948066067,-0.19338275286559314,-0.24514116653757334,-0.2618244031011425,-0.29586284787727024,-0.2972615922332986,-0.3307656967216239,-0.34748319829061414,-0.39394886741112956,-0.39825807666980495,-0.3997069903421058,-0.40236372413172505,-0.4531944601022806,-0.4686482839625872,-0.49194427862344314,-0.5115413995469194,-0.5375895775830686,-0.5695183082585689,-0.5744918245750403,-0.6065308712035504,-0.6368670278587389,-0.6458507511364582,-0.6754721648240318,-0.7006712860133155,-0.7228115706527687,-0.7444134584445137,-0.760511687989466,-0.8092044566532919,-0.8133547520649951,-0.8160132687148596,-0.8232675798565725,-0.8502566897227868,-0.8762428989283437,-0.8816822619511111,-0.8816663513585188,-0.8678639061924072,-0.8641667864603142,-0.8431195927676574,-0.8203969446694717,-0.8151158585187281,-0.8141980093911254,-0.8133547520649951,-0.779164202787467,-0.7610572229997943,-0.7444134584445137,-0.744130467509915,-0.7438779425889512,-0.7085741364128446,-0.6754721648240318,-0.6731772914809819,-0.6710765852748093,-0.6375977959781887,-0.6065308712035504,-0.6018514304643561,-0.5968361768777277,-0.562319404641086,-0.5375895775830686,-0.5209242445874867,-0.49266555323605,-0.47623147171294367,-0.4686482839625872,-0.4520447742487299,-0.42597818110817487,-0.3997069903421058,-0.3741386380212135,-0.34913974270349124,-0.3307656967216239,-0.32089393479916106,-0.28607556178324467,-0.26686480858939543,-0.2618244031011425,-0.252694631742286,-0.21351929340732312,-0.19288310948066067,-0.16214193715356195,-0.15022323507935864,-0.12394181586017927,-0.11207208097825472,-0.08566438506978713,-0.06475715749188993,-0.05500052223969787,-0.02360702622373889,-0.019555602365896263,0.013940771380783978,0.025503402330418812,0.04608409230518795,0.06955421587845922,0.08288206500126538,0.11421580987156466,0.12765963592572627,0.15182335862174723,0.15987413729298927,0.17758013026280972,0.20737186995434298,0.22076465224222863,0.25256474515106886,0.2565021937454648,0.28970594586271003,0.3076242396153286,0.3573216253132183,0.35864723948319144,0.35937261172718005,0.3616693089915404,0.41197939911696,0.42758853310367373,0.46134687626094584,0.4624076863916948,0.49652982672415513,0.5121544327296115,0.5447369981525729,0.5586733614646451,0.5654711203446365,0.5922407436958692,0.6018523663992128,0.6344124139651179,0.6441458498196346,0.6576178603195593,0.6836718632251659,0.7033537075855993,0.7230072162260996,0.7492160684900271,0.7621867917261445,0.7722950012060816,0.803914128784736,0.8185954796313948,0.841236294826563,0.8467676010523335,0.8598518767137393,0.8951547823442856,0.9101775884470444,0.9356130481523119,0.9503425257150071,0.9791188820675258,1.0127568510809088,1.0143681017347377,1.0480601756880072,1.077943227883995,1.0890118060022371,1.1170014693084895,1.133839423732376,1.1843723576989853,1.1856067774322638,1.185942762928971,1.1866480829661197,1.2355375970672626,1.2548840565494523,1.2828856249086953,1.30916711589937,1.3238253501699337,1.3286064009083867,1.3363997103700158,1.3702324893186364,1.3927666437904151,1.409619770454015,1.4291469606714577,1.4436786600239544,1.4617079374108974,1.473286216927558,1.4811881361544637,1.4895600721287878,1.4930399955167375,1.5042147454825714,1.5042147454825714,1.5041553753666066,1.5045467523907559,1.4953539224001395,1.4947338816797813,1.4863708824367632,1.4786874459007229,1.4111394637472592,1.3927666437904151,1.3874497585592116,1.3843883819450649,1.3628140152612729,1.3591213897345393,1.3358704507452566,1.3308022785944273,1.3238253501699337,1.297682227597567,1.2716124652062537,1.2632978012183584,1.2548840565494523,1.2217285407359832,1.2156290294930892,1.185942762928971,1.1781077360200158,1.1537156191597195,1.1266960821365823,1.1170014693084895,1.1026340534587207,1.069548369995395,1.0480601756880072,1.0206035963784008,1.0083114298195288,0.9791188820675258,0.945174762601249,0.9440668101563872,0.9101775884470444,0.8814367264880096,0.8692130268835245,0.841236294826563,0.8173389836405831,0.7941913812648722,0.7722950012060816,0.7541347727358931,0.7165977111973159,0.7033537075855993,0.6932611038665724,0.6441273211946714,0.6360106302594395,0.6344124139651179,0.6318028320457434,0.5816846012068289,0.5654711203446365,0.5340551558391806,0.5294926321422087,0.49652982672415513,0.4786779652511064,0.432831258398616,0.4288969353837735,0.42758853310367373,0.42507585050756846,0.3767279719603871,0.35864723948319144,0.32519368470311383,0.3236115509888049,0.28970594586271003,0.26950688868997164,0.231198234812362,0.22076465224222863,0.21427583372666215,0.18550037735059588,0.15736169978144998,0.15182335862174723,0.14358643976212937,0.09885358324171323,0.08288206500126538,0.05979981274302304,0.04002174457558727,0.013940771380783978,-0.018997652870270443,-0.022740132573827232,-0.05500052223969787,-0.07892385183436668,-0.10449257121302846,-0.12394181586017927,-0.13883063776346516,-0.18618649961494382,-0.19288310948066067,-0.19816772971714114,-0.22831383212209122,-0.25661181955599277,-0.2618244031011425,-0.2706146914315921,-0.31407832491861987,-0.3307656967216239,-0.3585044844645293,-0.37023678745663746,-0.3997069903421058,-0.42827606549739095,-0.44359229858028915,-0.4686482839625872,-0.49336516950709175,-0.5153055038859535,-0.5375895775830686,-0.5709659689045536,-0.5746008309791324,-0.6065308712035504,-0.6210680329370741,-0.6388264359852389,-0.6388264359852394,-0.6393158287288214,-0.6337530260997841,-0.6236286598181806,-0.6065308712035504,-0.5991312663006885,-0.5956145229996679,-0.5709619786891542,-0.5647521173301318,-0.5432619739774762,-0.5403211675647523,-0.5375895775830686,-0.5036676192317295,-0.49474386646797575,-0.4686482839625872,-0.4667265268039382,-0.46428709890240905,-0.4211076217403611,-0.3997069903421058,-0.3734222302159056,-0.34589963371982657,-0.3307656967216239,-0.32422495558867714,-0.30657208464798247,-0.27173918505915395,-0.2618244031011425,-0.24329257668718585,-0.21855180210036762,-0.19288310948066067,-0.16658466104347758,-0.14089056555290114,-0.12394181586017927,-0.11577633704516588,-0.09660583753184193,-0.06698803576721168,-0.05500052223969787,-0.02054867084061618,-0.02047159116924968,0.013940771380783978,0.026052465516190004,0.04833224494086075,0.07091174234859565,0.08288206500126538,0.11604835671195346,0.12155660661321788,0.15182335862174723,0.16261672780989267,0.18709355080475065,0.21077491074991928,0.22076465224222863,0.24305118440105522,0.2616645756359115,0.28970594586271003,0.31477540226702905,0.34109581037083503,0.35864723948319144,0.36972176557309444,0.4133082289553438,0.4247567824474383,0.42758853310367373,0.4330572345604806,0.4782056435269735,0.49652982672415513,0.5275825429904599,0.5402889408605742,0.5654711203446365,0.574590946324077,0.5888966993232763,0.6176485344568445,0.6344124139651179,0.6585386431639626,0.6903861587967399,0.6979382292737522,0.7033537075855993,0.7368210471521768,0.7460303163375408,0.7722950012060816,0.775489890780483,0.7796865331048362,0.8160275283855722,0.841236294826563,0.8586033805899684,0.8925736945202103,0.9044260457723765,0.9101775884470444,0.9211127032316839,0.9574495974753741,0.9791188820675258,1.0078578222028196,1.0182766678269757,1.0480601756880072,1.078122722851084,1.0878113328970866,1.1170014693084895,1.1370098339350032,1.1759787459124031,1.185942762928971,1.19114511471382,1.204349547192297,1.2408231799444773,1.2548840565494523,1.2867059672606502,1.2985908989040564,1.3238253501699337,1.3309044417875202,1.3409570044874504,1.367465347550279,1.3927666437904151,1.4016220810427469,1.4089954896614354,1.4195932030429623,1.4243000492778637,1.4383269160890753,1.4387659664782828,1.4392158342740076,1.440285140224924,1.4313529118041575,1.4295474945963558,1.4205116096994037,1.4111394637472592,1.3413479120212952,1.3238253501699337,1.3146201299615696,1.3080120962239454,1.2825796804366134,1.2548840565494523,1.2487346826606784,1.241073759493625,1.2088028336168954,1.185942762928971,1.1650996948482875,1.117067034340971,1.1170208170906037,1.1170014693084895,1.1169674662326048,1.0625884223829503,1.0480601756880072,1.0269752646080792,1.0038802242674314,0.9791188820675258,0.9475561601429701,0.9421359085414376,0.9101775884470444,0.8776814255828769,0.8734442895944174,0.841236294826563,0.8093173257767856,0.8038615464273096,0.7722950012060816,0.7413628859257195,0.7335707119658488,0.7033537075855993,0.6769155606723438,0.6576394322449741,0.6344124139651179,0.6166866656754135,0.56812576204609,0.5654711203446365,0.5639463938105052,0.561041132291185,0.5134620072310621,0.49652982672415513,0.4659415363073811,0.45030892440574055,0.42758853310367373,0.4193620737860182,0.4039591682028667,0.37090795663843634,0.35864723948319144,0.3322668422117929,0.320048519484772,0.28970594586271003,0.2678044912512312,0.23120669563862029,0.22076465224222863,0.2145795041319487,0.19103817007433355,0.15812204360964932,0.15182335862174723,0.1424288859196552,0.09889617868332978,0.08288206500126538,0.06040500083338873,0.03891629857884471,0.013940771380783978,-0.019008351365599196,-0.02184066836901799,-0.05500052223969787,-0.08467518433072652,-0.09560807599922905,-0.12394181586017927,-0.15081286590537113,-0.16754663885205145,-0.19288310948066067,-0.2208202708488085,-0.23462130121896152,-0.2618244031011425,-0.29464090315362723,-0.2991844262762853,-0.3307656967216239,-0.35097389676992163,-0.3893589213388382,-0.3893589213388382,-0.3773963920037722,-0.3704607938189035,-0.3467377800307947,-0.3307656967216239,-0.3052677233059402,-0.2663778928213807,-0.2630126290995509,-0.2618244031011425,-0.2592611625994241,-0.21119548185423964,-0.19288310948066067,-0.16103878516833703,-0.1522629447272199,-0.12394181586017927,-0.11070391554626235,-0.08127313310923512,-0.061818737558025916,-0.05500052223969787,-0.03701073468295357,-0.013351597506936486,0.013940771380783978,0.034080141378745044,0.07171036650579632,0.07925559575072594,0.08288206500126538,0.0941353641396625,0.1261298808239566,0.15182335862174723,0.17385141974931217,0.21804238478286964,0.22076465224222863,0.22212895191982218,0.2267380112779711,0.27700935195184373,0.28970594586271003,0.31012486713434795,0.33523420456630193,0.35864723948319144,0.3901753160133601,0.39584927605492615,0.42758853310367373,0.4572217185109362,0.469555158833892,0.49652982672415513,0.5145092287621584,0.5589830441820323,0.5637565979393675,0.5654711203446365,0.5729091010517062,0.6058843096553299,0.6344124139651179,0.6454033975875579,0.6562120994665137,0.6818075930390672,0.7033537075855993,0.7175404626970221,0.7308948094457839,0.7529375979956741,0.7722950012060816,0.789202872588207,0.8074384295010009,0.826508301955744,0.841236294826563,0.8672807417494952,0.9076705451423943,0.9092801167053044,0.9101775884470444,0.9122104175411603,0.9593425113130984,0.9791188820675258,1.00951175837838,1.0164520981225045,1.0480601756880072,1.0808135358615734,1.083988852720298,1.1170014693084895,1.1440978441664869,1.1631647443235527,1.185942762928971,1.1982858583961815,1.229206109020898,1.2465350779633249,1.2548840565494523,1.287573162961357,1.300796246780895,1.3238253501699337,1.3272535853916083,1.3308247457470324,1.3388131131804477,1.3529820764857319,1.3696423114244687,1.3708236822470838,1.3722493766505912,1.3740917118104155,1.3650852534177615,1.3617770510576714,1.3517948948544922,1.3413479120212952,1.265794319886759,1.2548840565494523,1.2340666138945413,1.2145276979766089,1.1987737193969061,1.185942762928971,1.1566611959528736,1.1331095387008463,1.1170014693084895,1.1117998476449684,1.0971782425467809,1.059373038045369,1.0480601756880072,1.030397432622331,1.000910753205679,0.9791188820675258,0.9525862419170807,0.9364591976225145,0.9101775884470444,0.8873788989731808,0.8598257303444625,0.841236294826563,0.8267182579192371,0.7744170226759564,0.7732660348690863,0.7722950012060816,0.7455578791465434,0.7278690817419498,0.7340200191637298,0.7361616576993684,0.7490137447471059,0.7583637820735745,0.7722950012060816,0.7844921888901699,0.7912373944205959,0.8136597032919979,0.841236294826563,0.8445585434766412,0.8472331272999649,0.8810566098069628,0.9101775884470444,0.9190067978734269,0.9321774466953943,0.9637431948640063,0.9791188820675258,1.008118183937905,1.0168111815418484,1.0480601756880072,1.0776654349997261,1.087094164202846,1.1170014693084895,1.147565949883417,1.1580308447532368,1.185942762928971,1.199739559660888,1.227404663164855,1.2423543060271727,1.2548840565494523,1.2749295485183185,1.290465204175438,1.293868652988635,1.2950257992853502,1.299623831621234,1.2875304837250563,1.2853837569615592,1.273711985095622,1.265794319886759,1.1956645445656044,1.185942762928971,1.1711892296768176,1.161477509481435,1.1357758828025042,1.1170014693084895,1.0916943351441737,1.0589435760751784,1.0480601756880072,1.039832638522642,0.9815654842569148,0.9791188820675258,0.9631509440628503,0.9418487227797967,0.9101775884470444,0.9057528540437221,0.9036916914052244,0.905162101477019,0.9101775884470444,0.9212619764441654,0.9247002732728986,0.9503059315014517,0.9791188820675258,0.9835709291409365,0.9896615235464838,1.032010827318238,1.0480601756880072,1.0704487023839548,1.094514143348825,1.1170014693084895,1.1329644568794053,1.1714758838920534,1.1771634859980753,1.185942762928971,1.1967134147482263,1.1999502303465364,1.1956645445656044]\n",
       "}\n",
       "}],\n",
       "\"theme\":{\n",
       "\"flavor\":\"high_contrast_dark\"\n",
       "}\n",
       "};\n",
       "           var plotContainer = document.getElementById(\"8EGlNU\");\n",
       "           window.letsPlotCall(function() {{\n",
       "               LetsPlot.buildPlotFromProcessedSpecs(plotSpec, -1, -1, plotContainer);\n",
       "           }});\n",
       "       })();    \n",
       "   </script>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "letsPlot(data) {x=\"x\"; y=\"y\"} + \n",
    " geomImshow(arr, extent=listOf(0.0, 8.0, -1.0, 3.0)) + \n",
    " geomDensity2D(color=\"yellow\") + \n",
    " ggsize(620, 300) + flavorHighContrastDark()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Flipping and transposing image using `extent`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "RasterData(225 x 225 x 3)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@file:DependsOn(\"com.github.jai-imageio:jai-imageio-core:1.3.0\")\n",
    "import javax.imageio.ImageIO\n",
    "import java.net.URL\n",
    "import org.jetbrains.letsPlot.geom.Extensions.create\n",
    "\n",
    "val img = ImageIO.read(\n",
    "    URL(\"https://github.com/JetBrains/lets-plot-docs/raw/master/source/examples/cookbook/images/fisher_boat.png\")\n",
    ")\n",
    "val fisherBoat = RasterData.create(img)\n",
    "fisherBoat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "   <div id=\"O2U5AS\"></div>\n",
       "   <script type=\"text/javascript\" data-lets-plot-script=\"plot\">\n",
       "       (function() {\n",
       "           var plotSpec={\n",
       "\"mapping\":{\n",
       "},\n",
       "\"ggsize\":{\n",
       "\"width\":700.0,\n",
       "\"height\":700.0\n",
       "},\n",
       "\"kind\":\"plot\",\n",
       "\"scales\":[],\n",
       "\"layers\":[{\n",
       "\"ymin\":100.0,\n",
       "\"mapping\":{\n",
       "},\n",
       "\"stat\":\"identity\",\n",
       "\"xmin\":0.0,\n",
       "\"ymax\":200.0,\n",
       "\"xmax\":100.0,\n",
       "\"show_legend\":false,\n",
       "\"href\":\"\",\n",
       "\"geom\":\"image\",\n",
       "\"data\":{\n",
       "}\n",
       "},{\n",
       "\"ymin\":100.0,\n",
       "\"mapping\":{\n",
       "},\n",
       "\"stat\":\"identity\",\n",
       "\"xmin\":100.0,\n",
       "\"ymax\":200.0,\n",
       "\"xmax\":200.0,\n",
       "\"show_legend\":false,\n",
       "\"href\":\"\",\n",
       "\"geom\":\"image\",\n",
       "\"data\":{\n",
       "}\n",
       "},{\n",
       "\"ymin\":0.0,\n",
       "\"mapping\":{\n",
       "},\n",
       "\"stat\":\"identity\",\n",
       "\"xmin\":0.0,\n",
       "\"ymax\":100.0,\n",
       "\"xmax\":100.0,\n",
       "\"show_legend\":false,\n",
       "\"href\":\"\",\n",
       "\"geom\":\"image\",\n",
       "\"data\":{\n",
       "}\n",
       "},{\n",
       "\"ymin\":0.0,\n",
       "\"mapping\":{\n",
       "},\n",
       "\"stat\":\"identity\",\n",
       "\"xmin\":100.0,\n",
       "\"ymax\":100.0,\n",
       "\"xmax\":200.0,\n",
       "\"show_legend\":false,\n",
       "\"href\":\"\",\n",
       "\"geom\":\"image\",\n",
       "\"data\":{\n",
       "}\n",
       "},{\n",
       "\"mapping\":{\n",
       "},\n",
       "\"stat\":\"identity\",\n",
       "\"yintercept\":100.0,\n",
       "\"color\":\"yellow\",\n",
       "\"position\":\"identity\",\n",
       "\"geom\":\"hline\",\n",
       "\"tooltips\":\"none\",\n",
       "\"data\":{\n",
       "}\n",
       "},{\n",
       "\"mapping\":{\n",
       "},\n",
       "\"stat\":\"identity\",\n",
       "\"color\":\"yellow\",\n",
       "\"position\":\"identity\",\n",
       "\"xintercept\":100.0,\n",
       "\"geom\":\"vline\",\n",
       "\"tooltips\":\"none\",\n",
       "\"data\":{\n",
       "}\n",
       "},{\n",
       "\"mapping\":{\n",
       "\"x\":\"x\",\n",
       "\"y\":\"y\",\n",
       "\"label\":\"label\"\n",
       "},\n",
       "\"stat\":\"identity\",\n",
       "\"data\":{\n",
       "\"x\":[50.0,150.0,150.0,50.0],\n",
       "\"y\":[200.0,200.0,0.0,0.0],\n",
       "\"label\":[\"original\",\"flip columns\",\"transpose\",\"flip rows\"]\n",
       "},\n",
       "\"position\":\"identity\",\n",
       "\"geom\":\"label\"\n",
       "}]\n",
       "};\n",
       "           var plotContainer = document.getElementById(\"O2U5AS\");\n",
       "           window.letsPlotCall(function() {{\n",
       "               LetsPlot.buildPlotFromProcessedSpecs(plotSpec, -1, -1, plotContainer);\n",
       "           }});\n",
       "       })();    \n",
       "   </script>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "val dim = 100\n",
    "\n",
    "val ext_base = listOf(0, dim, dim, dim + dim)\n",
    "val ext_flip_x = listOf(dim + dim, 0 + dim, 0 + dim, dim + dim)\n",
    "val ext_flip_y = listOf(0, dim, dim, 0)\n",
    "val ext_transpose = listOf(dim + dim, 0 + dim, dim, 0)\n",
    "\n",
    "val label_data = mapOf(\n",
    "    \"x\" to listOf(50, 150, 150, 50),\n",
    "    \"y\" to listOf(200, 200, 0, 0),\n",
    "    \"label\" to listOf(\"original\", \"flip columns\", \"transpose\", \"flip rows\")\n",
    ")\n",
    "\n",
    "(letsPlot() + \n",
    "     geomImshow(fisherBoat, extent=ext_base) + \n",
    "     geomImshow(fisherBoat, extent=ext_flip_x) + \n",
    "     geomImshow(fisherBoat, extent=ext_flip_y) + \n",
    "     geomImshow(fisherBoat, extent=ext_transpose) + \n",
    "        \n",
    "     geomHLine(yintercept=100, color=\"yellow\", tooltips=tooltipsNone) + \n",
    "     geomVLine(xintercept=100, color=\"yellow\", tooltips=tooltipsNone) + \n",
    "     geomLabel(data=label_data) {x=\"x\"; y=\"y\"; label=\"label\" } +\n",
    "     ggsize(700, 700)\n",
    ")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Kotlin",
   "language": "kotlin",
   "name": "kotlin"
  },
  "language_info": {
   "codemirror_mode": "text/x-kotlin",
   "file_extension": ".kt",
   "mimetype": "text/x-kotlin",
   "name": "kotlin",
   "nbconvert_exporter": "",
   "pygments_lexer": "kotlin",
   "version": "1.7.20-dev-1299"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
